Question

Two cars traveled the same distance. The first car travels at a rate of 42 mph and reaches its destination in t hours. The second car travels at a rate of 50 mph and reaches its destinations four hours earlier than the first car. How long does it take for the first car to reach its destination

Answer 1

25 hours

Explanation:

Let's denote the time it takes for the first car to reach its destination as "t" hours.

We know that the first car travels at a rate of 42 mph, so in t hours, it covers a distance of 42t miles.

The second car travels at a rate of 50 mph and reaches its destination four hours earlier than the first car. This means it takes (t - 4) hours for the second car to reach its destination.

In (t - 4) hours, the second car covers a distance of 50(t - 4) miles.

Since both cars traveled the same distance, we can set up an equation:

Distance traveled by the first car = Distance traveled by the second car

42t = 50(t - 4)

Now, let's solve for t:

42t = 50t - 200

Subtract 50t from both sides:

42t - 50t = -200

-8t = -200

Now, divide both sides by -8 to solve for t:

t = (-200) / (-8)

t = 25

So, it takes the first car 25 hours to reach its destination.