Person rides their bike to a park. His averages 25km/h on the way there & 20km/h on the way back. He rode for a total of 2.25 hours. How far is the park?

Answer 1

Use the formula Distance = Rate x time: D = RT, where Rate is the speed

Given: R1 = 25 kph, R2 = 20 kph, Total Time: T1 + T2 = 2.25 hours

The distance to the park is the same distance back home: D1 = D2

Equation 1: R1(T1) = R2(T2)

25(T1) = 20(T2)

Equation 2: T1 + T2 = 2.25

Use substitution to solve for either T1 or T2: T1 = 2.25 - T2

25(2.25 - (T2)) = 20(T2)

Distribute: 56.25 - 25(T2) = 20(T2)

Add 25(T2) to both sides of the equation: 56.25 = 45(T2)

Divide both sides by 45: T2 = 56.25/45 = 1.25 hr

Since the distances are equal, D = 20(1.25) = 25 km

Answer: distance = 25 km