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.
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
To find the cyclist's speed, we need to set up an equation based on the given information. Let's assume the cyclist's speed is denoted by S.
We know that the distance he travels on his first trip is 18 miles. So, the time it takes him to complete this trip is given by the formula:
Time = Distance / Speed
18 / S = T1
On his return trip, the distance is 23 miles, and he takes one hour longer than the first trip. So, the time for his return trip is given by:
Time = Distance / Speed
23 / S = T1 + 1
Now, we can set up an equation by equating T1 in both expressions:
18 / S = 23 / S - 1
To solve this equation, we can cross-multiply:
18(S - 1) = 23S
Simplifying:
18S - 18 = 23S
Bringing all the variables (S) to one side:
23S - 18S = 18
5S = 18
S = 18 / 5
So, the cyclist's speed is 3.6 miles per hour.