Question

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Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.

a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? _______________

Answer 1

Answer:

4r + 4(r + 3) = 68

r = 7 miles per hour

r + 3 = 10 miles per hour

Step-by-step explanation:

distance = rate * time

a)

4r + 4(r + 3) = 68

Distribute

4r + 4r + 12 = 68

8r + 12 = 68

8r = 56

r = 7 miles per hour

r + 3 = 10 miles per hour

Answer 2

a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68

b) The speed of both cyclists are 3mi/hr and 10mi/hr respectively

The formula for calculating the distance covered is expressed as:

Distance = speed * time

Let the speed covered by one cyclist be t

If one cycles 3 miles per hour faster than the other, the speed of the other will be t + 3

If both meet after 4 hours of riding, then their time will be 4 hours

Distance covered the first cyclist = 4r

Distance covered by the second = 4(r+3)

If the two cyclists are 68 miles apart, then:

4r + 4(r+3) = 68

a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68

b) Expand the equation in a to get "r"

4r + 4r + 12 = 68

8r + 12 = 68

8r = 68 - 12

8r = 56

r = 56/8

r = 7miles per hour

Speed of the first cyclist = 7mi/hr

Speed of the second cyclist = 3 + 7mi/hr = 10mi/hr

Hence the speed of both cyclists are 3mi/hr and 10mi/hr respectively

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