Question38) A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find his speed.
Studdy Solution
STEP 1
1. The cyclist travels at a constant speed both ways.
2. The distance of the first trip is 17 miles.
3. The distance of the return trip is 22 miles.
4. The return trip takes one hour longer than the first trip.
5. We need to find the cyclist's speed.
STEP 2
1. Define variables for speed and time.
2. Write expressions for the time taken for each trip.
3. Set up an equation relating the times.
4. Solve the equation for speed.
STEP 3
Define variables for speed and time.
Let be the speed of the cyclist in miles per hour.
Let be the time taken for the first trip in hours.
STEP 4
Write expressions for the time taken for each trip.
The time taken for the first trip is given by the formula:
The time taken for the return trip is:
STEP 5
Set up an equation relating the times.
Since the return trip takes one hour longer, we have:
STEP 6
Solve the equation for speed.
First, eliminate the fractions by multiplying the entire equation by :
Subtract 17 from both sides to isolate :
The cyclist's speed is:
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