SOLUTION: Stanley drove 240 miles at a certain rate of speed. If he had traveled 15 mph faster, he would have been able to travel 30 miles further in 3/4 of the time that he spent on his tri

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Question 524020: Stanley drove 240 miles at a certain rate of speed. If he had traveled 15 mph faster, he would have been able to travel 30 miles further in 3/4 of the time that he spent on his trip. What was Stanley's rate on the trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Stanley drove 240 miles at a certain rate of speed.
If he had traveled 15 mph faster, he would have been able to travel 30 miles further in 3/4 of the time that he spent on his trip.
What was Stanley's rate on the trip?
:
This is not hard, we can sum the problem up in an easy to understand statement:
"The fast car goes 270 mi in 3/4 of the time required by slow car to go 240 mi"
:
Let s = his speed on the trip
then
(s+15) = his faster speed
:
Write a time equation, Time = dist/speed
:
Fast car time = 3/4 slow car time
270%2F%28%28s%2B15%29%29 = 3%2F4*240%2Fs
Find 3/4 of 240, and you have:
270%2F%28%28s%2B15%29%29 = 180%2Fs
Cross multiply
270s = 180(s+15)
270s = 180s + 2700
270s - 180s = 2700
90s = 2700
s = 2700%2F90
s = 30 mph is the original speed
then
30 + 15 = 45 mph is the faster speed
:
We can check this by finding the time of each
270/45 = 6 hrs
240/30 = 8 hrs; 6 hrs is 3/4 of 8 hrs
:
:
How about that? Make perfect sense to you?