# math

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A cyclist bikes at a constant speed for 18 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 23 miles. Find his speed.

• math -

let his speed be x mph
time for first trip = 18/x
time for 2nd trip = 23/x

23/x - 18/x = 1
5/x=1
x = 5 mph

check:
to go 18 miles at 5 mph takes 3.6 hrs
to go 23 miles at 5 mph takes 4.6 hrs, which is 1 hour more

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