Average Speed problem

Question

a bus travels for 3 hours at an average speed of 50 mph. How much longer must the bus travel at an average speed of 60 mph so that the average speed for the total trip will be 52 mph?

Answer 1

average speed for 3 hours is 50, so distance travelled is 150 miles.  to average 60 mph in time t means that you will travel 60t miles.  Therefore, (150 +60t)/(t +3) = 52. 

Or stated in words, total distance divided by total time equals average speed.

 

solve by multiplying both sides by t+3

150 + 60t = 52t + 156

8t = 6

t=3/4 of an hour, or 45 minutes.