Math CentralQuandaries & Queries


Question from Mike:

if a 100 mile trip averages 50 miles per hour, how much distance does one need to travel at 90 miles per hour to decrease travel time by 10%

Hi Mike.

Overall travel time is 2 hours in the original trip (50 miles per hour for 100 miles). So 10% less time is 90% of 2 hours, which is 0.90 x 2 = 1.8 hours.

For the revised trip, you are going 90 mph for a ways, then 50 mph the rest of the way. Let's say you go x miles at 90 mph. Then you are left with 100 - x miles remaining to cover at 50mph.

Time equals distance divided by speed, so the time it takes for the 90 mph portion is x/90 hours and the time it takes for the 50 mph portion is (100-x)/50 hours. Therefore the total time is the sum of these, and that's what we want to make equal to the target total time of 1.8 hours:

1.8 = x/90 + (100 - x)/50 hours.

Can you solve for x from here and finish the question? I would start by multiplying bath sides by 450.

Stephen La Rocque and Harley.

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