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

Answer:

The van overtakes the truck at 2:15 PM.

Step-by-step 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

$65t = 45 + 45t$

$20t = 45$

$t = \frac{45}{20}$

$t = 2.25$

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

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