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A cyclist travels 20 miles at a second o...

A cyclist travels 20 miles at a second of 15 miles per hours. If he returns along the same path and the entire trip takes 2 hours, at what spped did he return?

A

15 mph

B

20 mph

C

22 mph

D

30 mph

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow the given information and apply the relevant formulas. ### Step 1: Calculate the time taken for the first part of the trip. The cyclist travels 20 miles at a speed of 15 miles per hour. We can use the formula for time: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \] For the first part of the trip: \[ t_1 = \frac{20 \text{ miles}}{15 \text{ miles per hour}} = \frac{20}{15} = \frac{4}{3} \text{ hours} \] ### Step 2: Set up the equation for the return trip. Let the speed of the cyclist on the return trip be \( s \) miles per hour. The time taken for the return trip can be expressed as: \[ t_2 = \frac{20 \text{ miles}}{s \text{ miles per hour}} = \frac{20}{s} \text{ hours} \] ### Step 3: Write the total time equation. The total time for the entire trip is given as 2 hours. Therefore, we can set up the equation: \[ t_1 + t_2 = 2 \] Substituting the values we have: \[ \frac{4}{3} + \frac{20}{s} = 2 \] ### Step 4: Solve for \( s \). First, we need to isolate \( \frac{20}{s} \): \[ \frac{20}{s} = 2 - \frac{4}{3} \] To subtract \( \frac{4}{3} \) from 2, we convert 2 into a fraction with a denominator of 3: \[ 2 = \frac{6}{3} \] Now, we can perform the subtraction: \[ \frac{20}{s} = \frac{6}{3} - \frac{4}{3} = \frac{2}{3} \] Next, we cross-multiply to solve for \( s \): \[ 20 \cdot 3 = 2 \cdot s \] \[ 60 = 2s \] \[ s = \frac{60}{2} = 30 \text{ miles per hour} \] ### Final Answer: The speed at which the cyclist returned is **30 miles per hour**. ---
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