Question

A van enters a highway going 60 mph, a truck enters at the same place 10 minutes later and drives 65 mph in the same direction. From the time the truck enters the highway, how long will it take to pass the van?

Answer 1

How much of a head start is 10min (1/6 hour) at 60 mph?

How long does it take at 5 extra mph to make up that head start?

Answer 2

What do you mean?

Answer 3

If traveling time of the van is t, the t-10/60 is the traveling time of the truck

60t = 65(t - 1/6)

solve for t

Answer 4

The first vehicle goes (1/6 hr)(60 miles/hour) = 10 miles head start

The second vehicle will reduce the difference of 10 miles by his more rapid speed of an extra 5 mph. 10 miles / 5 mph = time to catch up.

Answer 5

I still don't understand

Answer 6

A head start means the vehicles are now (10 min = 1/6 hr)(60 miles/hr) apart when the second vehicle gets going.

They go on and on, with the second vehicle going 5 mph faster than the leading vehicle. Eventually, the second vehicle catches the first, as his 5 mph eats into the lead of ten miles, taking 2 hours to make up the 10 mile original difference.

Answer 7

The truck will pass the van when the distances are equal.
Write the equation that says the distance of the van = the distance of the truck.
Solve the equation.

Answer 8

Seems the van has the longer time (t+1/6) as it starts first.

60(t+1/6) = 65 t

then my t = 2 hours comes out right

Answer 9

That is true. You can use t for the truck then the van will be t+1/6 or
you can use t for the van then the truck will be t-1/6

Answer 10

thank you everyone.