# 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

2.) 12 kph

Distance = 3 km

Rate = ?

Time = 15 mins (or 2.5 hrs)

3.) 7:12 am

Distance = 8 km

Rate = 40 kph

Time = ?

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

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

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

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

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

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