## Motion Problem Exercise Answer Key and Solution

Here’s the answer key and complete solution for Motion Problem Exercise 1.
1.) 1, 800 Kilometers

Distance = ?
Rate = 400 kph
Time = 4.5 hours $d = r \times t$ $d = 400 \ times 4.5$ $d = 1, 800 km$

2.) 12 kph

Distance = 3 km
Rate = ?
Time = 15 mins (or 2.5 hrs) $rate = \dfrac{distance}{time}$ $rate = \dfrac{3}{.25}$ $rate = 12 kph$

3.) 7:12 am
Distance = 8 km
Rate = 40 kph
Time = ? $time = \dfrac{distance}{rate}$ $time = \dfrac{8}{40}$
Time = 0.2 (or 12 minutes)

7:00 am + 12 minutes = 7:12 am

4.) 2 hours and 30 minutes or 2 1/2 hours
Rate Time Distance
Rey
rate = 55 kph
time = t
distance = 55t kph
Maco
rate = 45 kph
time = t
distance = 45t kph

Distance 1(Rey) + Distance 2(Maco) = Total distance
55t km/hr + 45t km/hr =250 km
100t km/hr = 250 km $\dfrac{250 km}{100 km/hr}$
t = 2.5 hrs or 2 hrs and 30 minutes

5.) 2.4 hrs or 2 hrs and 24 minutes
Car 1
rate = 40 kph
time = t
distance = 40t kph
Car 2
rate = 30 kph
time = t
distance = 30t kph

Distance 1(Car 1) + Distance 2(Car 2) = Total distance
40t km/hr + 30t km/hr =168 km
70t km/hr = 168 km $= \dfrac{168km}{70 km/hr}$
t = 2.4 hrs or 2 hrs and 24 minute

6.) 4 hours
Car 1
rate = 55 kph
time = t
distance = 55t kph
Car 2
rate = 40 kph
time = t
distance = 40t kph

Distance 1(Car 1) – Distance 2(Car 2) = Total distance
55t km/hr – 40t km/hr = 60 km
15t km/hr = 60 km $\dfrac{60 km}{15km/hr}$
t = 4

7.) 4 hours
Bill
rate = 30 kph
time = t + 4
distance = 30(t + 4) kph
John
rate = 60 kph
time = t
distance = 60t kph

Distance 1(Bill) = Distance 2(John)
30(t + 4) = 60t
30t + 120 = 60t
30t – 60t = -120
-30t = -120 $\dfrac{-120}{-30}$
t = 4 hours

8.) 4 hours
Car A
rate = 40 kph
time = t + 2
distance = 40(t + 2) kph
Car B
rate = 60 kph
time = t
distance = 60t kph
Distance 1(Car A) = Distance 2(Car B)
40(t + 2) = 60t
40t + 80 = 60t
40t – 60t = -80
-20t = -80 $\dfrac{-80}{-20}$
t = 4 hours

9.) 262.5 Kilometers
D = RT
D = 75kph × 3.5hrs
D = 262.5 km

10.) 2 hours and 30 minutes or 2 1/2 hours
Car
rate = 40 mph
time = t
distance = 40t mph
Bus
rate = 60 mph
time = t
distance = 60t mph

Distance 1(Car) + Distance 2(Bus) = Total distance
40tm/hr + 60t m/hr =250 m
100t m/hr = 250 m
t= (250 m)/(100 m/hr)
t=2.5 hrs or 2 hrs and 30 minuteS