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James travels 40 km using a motorcycle. For the same amount of time, Alen travels 15 km using his bicycle. If James travels 20 km/h faster than Alen, find the rate of Alen.

A) 20 km/h
B) 15 km/h
C) 10 km/h
D) 5 km/h

User Nhan Cao
by
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1 Answer

6 votes

Final answer:

Alen's rate is found to be 15 km/h by setting up and solving an equation based on the given distances and the information that James's speed is 20 km/h faster than Alen's. Both parties travel for the same duration, allowing the calculation of their respective speeds.

Step-by-step explanation:

To find the rate of Alen, we need to use the given information and apply the concept of speed, which is distance divided by time. Since James and Alen travel for the same amount of time:

Let t = the time both James and Alen travel.

James's speed = (distance James travels) / t = 40 km / t

Alen's speed = (distance Alen travels) / t = 15 km / t

We're told James travels 20 km/h faster than Alen. This gives us the equation:

Alen's speed + 20 km/h = James's speed

Substitute the expressions for their speeds:

15 km / t + 20 km/h = 40 km / t

Solving for t, we get:

t = 1 hour

Now, substituting t back into Alen's speed expression:

Alen's speed = 15 km / 1 h = 15 km/h

The rate of Alen is 15 km/h, which corresponds to option B.

User Harrison Xi
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