Question

Greg and Ian started out at their houses and are biking towards each other. Greg started first, and has already gone 5 miles. He bikes at a constant speed of 3 miles per hour. Ian left, and rides at 4 miles per hour. When the boys meet halfway between their houses, they will continue to the park together. How long will that take? How far will each boy have ridden?

A. It will take 2.5 hours, and each boy will have ridden 6.25 miles.
B. It will take 1 hour, and each boy will have ridden 7 miles.
C. It will take 2 hours, and each boy will have ridden 5 miles.
D. It will take 3 hours, and each boy will have ridden 8 miles.

Answer 1

After calculating, Greg and Ian's combined closing speed is 7 mph. It will take approximately 43 minutes for them to meet, during which Greg will have ridden approximately 7.14 miles and Ian will have ridden approximately 2.86 miles. However, these calculations do not match the provided answer choices.

Step-by-step explanation:

To determine how long it will take for Greg and Ian to meet each other halfway and how far each boy will have ridden, let's define the situation as a problem of relative motion. We know that Greg has already biked 5 miles before Ian started, and Greg bikes at 3 miles per hour while Ian bikes at 4 miles per hour.

First, we need to find the total distance between their houses. Since they meet halfway, we can double the distance Greg already covered to get the total distance, which is 5 miles * 2 = 10 miles. Now, we'll determine the time it takes for them to meet.

The boys are approaching each other, so their speeds add up when calculating the closing speed. The combined speed at which they are closing the gap is 3 mph + 4 mph = 7 mph. To cover the remaining half of the distance, which is 5 miles (half of 10 miles), it will take 5 miles / 7 mph = 0.714 hours, or approximately 43 minutes.

For the distance traveled, Greg will have ridden his original 5 miles plus additional miles during the 43 minutes. Greg's additional distance is 3 mph * 0.714 hours = 2.14 miles. So, Greg will have ridden 5 miles + 2.14 miles = 7.14 miles. Ian, on the other hand, will have only been traveling for the 43 minutes, so he will have ridden 4 mph * 0.714 hours = 2.86 miles.

Since none of the provided answer choices match the calculated values, it suggests there may be an error in the question or answer choices given.