Question

My trip to work is 120 miles. If i go 8 mph faster than my usual speed, i'll get to work 30 minutes earlier. How long does my trip take, in hours, if i go my usual speed?

Answer 1

My trip to work is 120 miles. If I go 8 mph faster than my usual speed,

I'll get to work 30 minutes earlier.

How long is my trip if I don't speed up, in hours?

:

Let s = his normal speed

then

(s+8) = the faster speed

;

Change 30 min to .5 hrs

:

Write a time equation; time = dist/speed

normal time - faster time = .5 hrs

120%2Fs - 120%2F%28%28s%2B8%29%29 = .5

multiply by s(s+8), results:

 

120(s+8) - 120s = .5s(s+8)

120s + 960 - 120s = .5s^2 + 4s

arrange as a quadratic equation on the right

0 = .5s^2 + 4s - 960

multiply by 2 to get the coefficient of s^2 to = 1

s^2 + 8s - 1920 = 0

Factors to

(s-40)(s+48) = 0

the positive solution

s = 40 mph is his normal speed

then

120/40 = 3 hrs is his normal time

:

We can confirm this by finding the time at the faster speed

120/48 = 2.5 hrs, a half hour sooner