Question

Let's revisit the story about you and your cheating ex-friend's skateboarding experience. In order to get even, you challenge him to a rematch. This time you challenge your friend to a bike race. You know your friend and anticipate he will cheat again. So you plan on beating him at his own game. You take a 15-foot head start and go 7 feet per second. Your friend, who also cheats, gets a head start of 25 feet and goes 5 feet per second. How much time would it take you to catch up to your cheating ex-friend? How far from the starting line will you be when you catch up to him?

a) Time: 5 seconds, Distance: 10 feet
b) Time: 10 seconds, Distance: 50 feet
c) Time: 15 seconds, Distance: 75 feet
d) Time: 3 seconds, Distance: 15 feet

Answer 1

It will take you 5/6 seconds to catch up to your cheating ex-friend. You will be 5 5/6 feet from the starting line.

Step-by-step explanation:

To calculate how long it will take you to catch up to your cheating ex-friend, we need to determine when you reach the same position as him. You have a head start of 15 feet and travel at a speed of 7 feet per second. Your friend has a head start of 25 feet and travels at a speed of 5 feet per second.

Let's set up an equation to represent the situation:

Distance = Speed × Time

Your distance = Your speed × Time

Your friend's distance = Your friend's speed × Time

Since the two distances are equal when you catch up, we can set up the equation:

15 + 7T = 25 + 5T

Where T is the time it takes for you to catch up to your friend.

Simplifying the equation

12T = 10

T = 10/12

T = 5/6 seconds

Therefore, it will take you 5/6 seconds to catch up to your cheating ex-friend. To determine how far from the starting line you will be when you catch up to him, we can substitute the value of T into one of the equations:

Your distance = 7 × (5/6)

Distance = 35/6

Distance = 5 5/6 feet