Question

3. A truck leaves a depot at 11 AM and travels at a speed of 45 mph. At noon, a van leaves

the same place and travels the same route at a speed of 65 mph. At what time does the van
overtake the truck?​

Answer 1

The van overtakes the truck at 2:15 PM.

Explanation:

A truck leaves a depot at 11 AM and travels at a speed of 45 mph.

The van leaves 1 hour later, so when the van leaves, the truck will be at position 45 miles. The equation for the truck's position is given by:

`T(t) = 45 + 45t`

At noon, a van leaves the same place and travels the same route at a speed of 65 mph.

At noon, the van is at the position of 0 miles, and travels at a speed of 65 miles per hour. So, the equation for the vans' position is:

`V(t) = 65t`

At what time does the van overtake the truck?​

t hours after noon, in which t is found when:

`V(t) = T(t)`

So

`65t = 45 + 45t`

`20t = 45`

`t = (45)/(20)`

`t = 2.25`

0.25 of an hour = 1/4 = 15 minutes.

Thus, the van overtakes the truck at 2:15 PM.