SOLUTION: A car drove from one city to another and returned by different route. The outward journey was 48 km and the return journey was 8 km shorter. The speed of the car on the return jou

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Question 541106: A car drove from one city to another and returned by different route. The outward journey was 48 km and the return journey was 8 km shorter. The speed of the car on the return journey increased by 4 km/h. The return journey took one hour less time. Find the speed of the car on the outward journey.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A car drove from one city to another and returned by different route.
The outward journey was 48 km and the return journey was 8 km shorter.
The speed of the car on the return journey increased by 4 km/h.
The return journey took one hour less time.
Find the speed of the car on the outward journey.
:
let t = time of the outward journey (48 km)
then
(t-1) = time of the return journey (40km)
:
Write speed equation, speed = dist/time
:
return speed - outbound speed = 4 km/hr
40%2F%28%28t-1%29%29 - 48%2Ft = 4 km
:
multiply by t(t-1), results:
40t - 48(t-1) = 4t(t-1)
40t - 48t + 48 = 4t^2 - 4t
-8t + 48 = 4t^2 - 4t
0 = 4t^2 - 4t + 8t - 48
:
A quadratic equation
4t^2 + 4t - 48 = 0
:
Simplify, divide by 4
t^2 + t - 12 = 0
:
factors to:
(t+4)(t-3) = 0
:
The positive solution
t = 3 hrs travel time of the outbound journey
Find the speed
48%2F3 = 16 km/hr speed on the outbound journey
:
:
Confirm this solution by finding the speed on the return journey
40%2F2 = 20 km/hr, a 4 km/hr difference