Formula DRT
Grade 3+
Get the Gyro JiJi to land under the laser boxes.................. and the ballon will pop.
15 ft
? sec
Gyro JiJi Blue needs to go a distance of 15 feet. Gyro JiJi Blue travels at a speed of 3 feet/second.
How long should Gyro JiJi Blue travel to end up under the laser box, so it will pop the balloon?
10 ft
? sec
25% of 5 ft/sec
The max speed of Gyro JiJi Red is 5 feet/second. If Gyro JiJi Red needs to travel 10 feet and travels at
25% of its max speed, how long does it take to end up under the laser box, so it will pop the balloon?
Get both Gyro JiJis to pass under the balloon popper at the same time to make the balloon pop.
? ft
3 ft/sec
15 ft
2 ft/sec
Gyro JiJi Red travels at 3 feet/second. Gyro JiJi Blue travels at 2 feet/second. Gyro JiJi Red and Gyro JiJi
Blue are 15 feet apart. They both start at the same time. Where should you place the balloon popper, so
both Gyro JiJis pass under it at the same time and pop the balloon?
3 ft
? ft
75% of Sphero Blue speed
Gyro JiJi Red is 3 feet ahead of Gyro JiJi Blue and travels at 75% of Gyro JiJi Blue’s speed. They both start at
the same time. Where should you place the balloon popper so both Gyro JiJi pass under it at the same time?
© MIND Research Institute
FORMULA DRT- SOLUTIONS
For Internal Use Only. MIND Research Institute Confidential & Proprietary
For Internal Use Only. MIND Research Institute Confidential & Proprietary
1
1
1
Gyro JiJi
For
Internal
Use Only. MIND Research Institute Confidential & Proprietary
Gyro
JiJi
15 ft
? sec
Question: Gyro JiJi Blue needs to go a distance of 15 feet. Gyro JiJi Blue travels at a speed of 3
Gyro
JiJi Blue needs
goBlue
a distance
ofto15go
feet.
Gyro JiJi Blue
travels
a speed
3 feet/second.
long of 3
Question:
Gyro
JiJi
needs
a Blue
distance
ofto15end
feet.
JiJi
travels
awill
speed
feet/second.
Howto
long
should
Gyro
JiJi
travel
upatGyro
under
theofBlue
laser
box, soatitHow
pop the
should
Gyro
JiJi
Blue
travel
to
end
up
under
the
laser
box,
so
it
will
pop
the
balloon?
Gyro
JiJi
feet/second.
How long should Gyro JiJi Blue travel to end up under the laser box, so it will pop the
balloon?
balloon?
Question: Gyro JiJi Blue needs to go a distance of 15 feet. Gyro JiJi Blue travels at a speed of 3
Intuitive Solution: Every second, Gyro JiJi Blue travels 3 feet. Counting by 3’s to get to 15, it takes
feet/second.
How longEvery
should
Gyro Gyro
JiJi Blue
traveltravels
to end3 up
under
the laser
box,
the
Intuitive
Solution:
second,
JiJi Blue
feet.
Counting
by 3’s
to so
getittowill
15, pop
it takes
5 seconds
(counting
by three’s
5 times)
to travel
15 ft.
5balloon?
seconds (counting by three’s 5 times) to travel 15 ft.
Algebraic Solution: For distance, constant rate, and time we use the formula that distance =
Intuitive Solution:
Every
second, Gyro
JiJi Blue
travels
3 feet.
Counting
3’s to that
get todistance
15, it takes
feet
Algebraic
Solution:
For
constant
rate,
and and
time
the. by
formula
=
rate
× time
or
d =byrt.three’s
Fordistance,
this
problem,
d =
15feet
r we
= 3use
This gives,
15 = 3t. So
second
5 seconds
(counting
5
times)
to
travel
15
ft.
feet
×=time
or d = rt. For this problem, d = 15feet and r = 3 second . This gives, 15 = 3t. So
trate
= 15
5 seconds.
3
15
t = 3 = 5 seconds.
Algebraic Solution: For distance, constant rate, and time we use the formula that distance =
feet
rate × time or d = rt. For this problem, d = 15feet and r = 3 second
. This gives, 15 = 3t. So
t = 15
=
5
seconds.
3
? feet
sec
The max speed of Gyro JiJi Red is 5 feet/second. If Gyro JiJi Red needs to travel 10
Question:
The
max
of
Gyro
JiJilong
Red
is 5 feet/second.
Gyro
JiJi
Red
needs
to so
travel
10of
feet
andmax
travels
itsspeed
maxisspeed,
how
does
it take
endIfto
up
under
box,
will
pop
The
speedatof25%
Gyroof
JiJi
Red
5 feet/second.
If Gyro
JiJi
Redto
needs
travel
10the
feetlaser
and
travels
atit25%
and
travels
at
25%
of
its
max
speed,
how
long
does
it
take
to
end
up
under
the
laser
box,
so
it
will
pop
balloon?
itsthe
max
speed, how long does it take to end up under the laser box, so it will pop the balloon?
the balloon?
Question: The max speed of Gyro JiJi Red isfeet5 feet/second. If Gyro JiJi Red needs to travel 10 feet
Solution: Gyro JiJi Red is travelling at 1.25 second because (0.25)×5 = 1.25. Using the same d = rt
andSolution:
travels at Gyro
25% JiJi
of its max
speed, how
feet it take to end up under the laser box, so it will pop
10 does
is travelling
at long
1.25
because (0.25)×5 = 1.25. Using the same d = rt
equation as above,
10 =Red
1.25t
and so t =
=
8 seconds.
second
1.25
the
balloon?
10
equation as above, 10 = 1.25t and so t = 1.25 = 8 seconds.
25% Question:
of 5 ft/sec
feet
Solution: Gyro JiJi Red is travelling at 1.25 second
because (0.25)×5 = 1.25. Using the same d = rt
10
equation as above, 10 = 1.25t and so t = 1.25 = 8 seconds.
? ft
Question: Gyro JiJi Red travels at 3 feet/second. Gyro JiJi Blue travels at 2 feet/second. Gyro JiJi
Gyro JiJi Red travels at 3 feet/second. Gyro JiJi Blue travels at 2 feet/second.
RedQuestion:
and3Gyro
should you Gyro
place JiJi
the
ft/sec JiJi Blue are 15 feet apart. They both start at the same time. Where
2 ft/sec
Red
andpopper,
Gyro JiJi
15JiJis
feet pass
apart.under
Theyitboth
start
at the
same
Where
should you place the
balloon
soBlue
both are
Gyro
at the
same
time
and time.
pop the
balloon?
balloon popper, so both Gyro JiJis pass under it at the same time and pop the balloon?
Gyro
Red travels
at 3JiJi
feet/second.
JiJi Blue travels
at 2Red
feet/second.
Gyro
JiJiare
Gyro Question:
JiJi Red travels
at JiJi
3 feet/second.
Gyro
Blue travelsGyro
at 2 feet/second.
Gyro JiJi
and Gyro JiJi
Blue
Solution:
Both
balls
travel
for
the
same
amount
of
time.
Each
second,
the
two
roll
closer
to
each
15Red
feetand
apart.
They
both
start at 15
thefeet
sameapart.
time.They
Whereboth
should
the balloon
popper,
so bothyou
Gyro
JiJisthe
pass
Gyro
JiJi
Blue
startyou
at place
theEach
same
time. Where
should
place
feet
Solution:
Both
ballsare
travel
forSo,
thethey
same
time.
second,
two
closer
to each
other
and
use
up atime
total
of
5 feet.
areamount
movingoftogether
at a speed
of the
5 second
. roll
There
are 15
total
under
it
at
the
same
and
pop
the
balloon?
balloon popper,
so
both of
Gyrofeet.
JiJisSo,
pass
under moving
it at the same
time and
pop of
the5balloon?
feet
other
use up
a total
together
a speed
. There This
are 15
total
feel toand
travel,
so it
takes 3 5seconds
forthey
the are
balls to meet.
Each at
ball,
travels
forsecond
3 seconds.
means
feel
to travel,
so itpopper
takes 93 feet
seconds
the Gyro
balls to
Each6 ball,
travels
for Gryo
3 seconds.
Thisbecause
means
that we
need the
awayfor
from
JiJimeet.
Red and
feet away
from
JiJi Blue
Solution:
Both
balls travel
for
thefrom
sameGyro
amount
of time.
Each
second,
the Gryo
two roll
closer
to each
that
we
need
the
popper
9
feet
away
JiJi
Red
and
6
feet
away
from
JiJi
Blue
because
of the equation d = rt.
feet
other
use upd a=total
of theand
equation
rt. of 5 feet. So, they are moving together at a speed of 5 second . There are 15 total
feel to travel, so it takes 3 seconds for the balls to meet. Each ball, travels for 3 seconds. This means
dred = rt = 3 × 3 = 9 and dblue = rt = 2 × 3 = 6.
that
need
9 feet
Gyro
dred we
= rt
= 3the
× 3popper
= 9 and
dblueaway
= rtfrom
=2×
3 =JiJi
6. Red and 6 feet away from Gryo JiJi Blue because
of the equation d = rt.
dred = rt = 3 × 3 = 9 and dblue = rt = 2 × 3 = 6.
3 ft
For Internal Use Only. MIND Research Institute Confidential & Proprietary
? ft
75% of Sphero Blue speed
Question: Gyro JiJi Red is 3 feet ahead of Gyro JiJi Blue and travels at 75% of Gyro JiJi Blue’s
speed.
They
start
at the
sameJiJi
time.
should
youofplace
popper
both
Gyro
JiJi
Gyro JiJi
Redboth
is 3 feet
ahead
of Gyro
BlueWhere
and travels
at 75%
Gyro the
JiJi balloon
Blue’s speed.
Theysoboth
start
at the
sameunder
time. Where
should
place the balloon popper so both Gyro JiJi pass under it at the same time?
pass
it at the
sameyou
time?
Intuitive Solution: The extra speed that Gyro JiJi Blue has needs to use up 3 feet, this extra speed
is 25% of its own speed. Because they are both rolling for the same about of time, the 25% additional
speed means 25% additional distance. So, we need that 25% gives us 3 feet. Proportionally, 50% gives
us 6 feet, 75% gives us 9 feet, and 100% gives us 12 feet. Gyro JiJi Blue will travel 12 feet and then the
two will be at the same popper. Gyro JiJi Red will have to travel just 9 feet.
Algebraic Solution: We will use letters to represent the respective distances, rates, and times for
each Gyro JiJi.
dr = distance for Gyro JiJi Red
rr = rate for Gyro JiJi Red
tr = time for Gyro JiJi Red
db = distance for Gyro JiJi Blue
rb = rate for Gyro JiJi Blue
tb = time for Gyro JiJi Blue
What we know:
db = dr + 3. Gyro JiJi Blue needs to travel 3 more feet than Gyro JiJi Red.
tb = tr . Since they are the same, let’s just use t for time and save the hassle of red versus blue.
rr = (0.75)rb . Gyro JiJi Red travels at 75% of Gyro JiJi Blue’s speed.
Using the formula for distance = rate × time and using t for both gyro JiJi’s we have:
db = dr + 3
rb t = r r t + 3
r b t − rr t = 3
(rb − rr )t = 3
(rb − (0.75)rb )t = 3
(0.25)rb t = 3
( 14 )rb t = 3
rb t = 3 × 4. Remember that db = rb × t
db = 12
Gyro JiJi Blue travels 12 feet.
© MIND Research Institute