From some point A a car traveling at 50mph starts toward some point B 500 miles away 2 hours later a second car at point B starts traveling at 30mph towards A when will the cars meet?

Answer 1

You really should attempt to solve this on your own before reading this answer, otherwise you will not learn the lesson. Read and understand each step before proceeding past that step.

If car A starts travelling 50mph towards another car B 500 miles away, and the second car starts two hours later towards the first car at 30mph, and can find the meeting time with a system of simultaneous equations in two unknowns.

Start by writing down what you know.

If car A travels at 50, then its distance as a function of time is 50T, so XA = 50T.

If car B travels at 30, but starting two hours later, its distance as a function of time is 30(T-2), so XB = 30(T-2) = 30T - 60.

The two cars travel 500 miles and meet, so XA + XB = 500.

Plug the values of XA and XB into XA + XB = 500.

This gives 50T + 30T - 60 = 500.

Solve for T.

The answer is 7. The cars meet after seven hours.

Cross check:

In seven hours, car A goes 7 times 50, or 350 miles.

In five hours, car B goes 5 times 30, or 150 miles.

150 + 350 is 500.