Question

Mike and Jane leave their home on bikes traveling in opposite directions on a straight road. Mike rides 5 mi/h faster than Jane. After 4 h, they are 124 mi apart. At what rate does Mike ride his bike?

a) 29 mi/h
b) 24 mi/h
c) 25 mi/h
d) 22 mi/h

Answer 1

By setting up an equation, we find that Mike's biking rate is 18 mi/h, which is not one of the provided options. It seems there may be an inconsistency with the options given for the problem.

Step-by-step explanation:

To determine Mike's biking rate, let's define the rate at which Jane rides as x miles per hour (mi/h). Since Mike rides at a rate that is 5 mi/h faster than Jane, his rate is x+5 mi/h. After 4 hours, the distance between Mike and Jane can be represented as 4(x) + 4(x+5).

Given that they are 124 miles apart, the equation can be set up as:

4(x) + 4(x+5) = 124

8x + 20 = 124

8x = 104

x = 13

Now that we found Jane's rate to be 13 mi/h, we add 5 mi/h to get Mike's rate:

Mike's biking rate = 13 mi/h + 5 mi/h = 18 mi/h.

However, looking back at this result and the options provided, there seems to be a miscalculation as the answer of 18 mi/h is not an option given. So, let's re-examine our calculations:

4(x) + 4(x+5) = 124

4x + 4x + 20 = 124

8x = 104

8x = 104

x = 13 (Jane's rate)

Mike's rate = x + 5 = 13 mi/h + 5 mi/h = 18 mi/h is the correct value of Mike's rate.

Thus, unfortunately, all the provided options a) 29 mi/h, b) 24 mi/h, c) 25 mi/h, and d) 22 mi/h are incorrect.