Question 648824

Travel by car: Marcus drives from one town to another in 6 hours. On the return trip, his speed increased by 10 mph and the trip takes 5 hours. Find his rate on the return trip. How far apart are the towns? 

So far I know:
rate x time= distance
Going trip- rate= r   time =6  distance= ?
Return trip-  rate= r+10   time= 5  distance=? 

I am not sure how to proceed in writing and solving the equation.


Let the town he left from be town A and the town he went to, town B
Let rate of speed from town B to town A, be S
Then speed from town A to town B = S - 10 

Distance from town A to town B equals distance from town B to town A, OR 

6(S – 10) = 5S

6S – 60 = 5S 

6S – 5S = 60 


S, or speed on return trip (from town B to town A) = {{{highlight_green(60)}}} mph 


Distance between the towns = 6(60 – 10), or 5(60), or {{{highlight_green(300)}}} miles.


You can do the check!!


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