Question

2. Two bicyclists on a 75-mile trail ride toward each other. One bicyclist

begins at the 45-mile marker. The other begins at the end of the trail. The
expressions shown represent the distance from the Parking Lot for each
A. Write an equation to represent the bicyclists' meeting after x hours.
plify.
bicyclist when they meet.
B. After how many hours do the bicyclists meet?
Parking
Lot
75 - 10x
45 + 10x
75 mi
C. How far away are the bicyclists from the
parking lot when they meet?

Answer 1

A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x

B. The bicyclist meet after 1.5 hours

C. They were 60 miles from the parking lot when they meet

Explanation:

A. The starting location of the one of the bicyclist = 75-mile marker

The starting location of the other bicyclist = 45-mile marker

The direction of motion of the bicyclist = Towards each other

The time after which the bicyclist meet = x hours

The expression for the distance from the parking lot are

75 - 10x and 45 + 10x

Whereby the bicyclist are have the same speed, v, we have;

The location where they meet is 75 - v×x = 45 + v×x

B. Solving for x, we have;

75 - v×x = 45 + v×x

75 - 45 = v×x + v×x = 2×v×x

30 = 2×v×x

x = 30/(2×v)

Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;

x = 30/(2×v) = 30/(2×10) = 1.5

x = 1.5 hours

The bicyclist meet after 1.5 hours

C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;

75 - 10 × 1.5 = 60 miles

45 + 10 × 1.5 = 60 miles

Therefore, they were 60 miles from the parking lot when they meet.

Answer 2

A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x

B. The bicyclist meet after 1.5 hours

C. They were 60 miles from the parking lot when they meet

Explanation:

A. The starting location of the one of the bicyclist = 75-mile marker

The starting location of the other bicyclist = 45-mile marker

The direction of motion of the bicyclist = Towards each other

The time after which the bicyclist meet = x hours

The expression for the distance from the parking lot are

75 - 10x and 45 + 10x

Whereby the bicyclist are have the same speed, v, we have;

The location where they meet is 75 - v×x = 45 + v×x

B. Solving for x, we have;

75 - v×x = 45 + v×x

75 - 45 = v×x + v×x = 2×v×x

30 = 2×v×x

x = 30/(2×v)

Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;

x = 30/(2×v) = 30/(2×10) = 1.5

x = 1.5 hours

The bicyclist meet after 1.5 hours

C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;

75 - 10 × 1.5 = 60 miles

45 + 10 × 1.5 = 60 miles

Therefore, they were 60 miles from the parking lot when they meet.