A compact car is driven 144mi. If it had traveled 4mph faster, it could have made the trip in 1/2 hour less time. What was the speed of the car?

Answer 1

Recall that rate is distance traveled over time, or
r = d/t
Solving for distance, we have
d = rt

Let r = speed of car
Let t = time it takes to travel 144 miles
Thus,
rt = 144 ; equation (1)

If it had traveled 4 mph faster, time it takes to travel the same distance would be less by 1/2 hr. In equation,
rt = (r + 4)(t - 1/2)

Solving,
rt = rt - 0.5r + 4t - 2
0 = 0 - 0.5r + 4t - 2
r = 8t - 4

Substituting this to equation (1),
rt = 144
(8t - 4)(t) = 144
8t^2 - 4t - 144 = 0
2t^2 - t - 36 = 0

Now solve for t. Note that t has 2 roots, one positive and one negative. Of course we want the positive, because time cannot be negative.
After getting the positive root of t, substitute this to equation (1) to solve for r.

Hope this helps~ :3

Answer 2

original speed --- x mph
time at original speed = 144/x hrs

new speed = x+4
time at new speed = 144/(x+4)

144/x - 144/(x+4) = 1/2
solve for x
let me know what you get.