# College algebra

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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

• College algebra -

let the 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

his speed is 5 mph

check:
time for 1st trip = 18/5 = 3.6 hrs
time for 2nd trip = 23/5 = 4.6 hrs, which is 1 hour more

• College algebra -

Let X be distance per hour,
Ist trip=18miles =18/X
2nd trip=23miles =23/X,=1hr longer
speed,S=2nd trip-1st trip
X=23-18
X=5mph.

checkings
23/5 -18/5 =4.6-3.6=1hr

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