Question

A car leaves Angola 1.5 hours after a truck and goes in the same direction. The car travels 65 miles per hour while the truck travels 50 miles per hour. How long will it take the car to catch up to the truck?

Answer 1

So, the car is traveling at a faster speed than the truck. Since they are both traveling in the same direction, the car will gradually catch up to the truck. To find out how long it will take for the car to catch up, we can use the concept of relative speed. The relative speed between the car and the truck is the difference between their speeds, which is 65 - 50 = 15 miles per hour. To find the time it takes for the car to catch up, we can divide the distance between them (which is the initial time difference of 1.5 hours multiplied by the truck's speed of 50 miles per hour) by the relative speed of 15 miles per hour. So, it will take the car (1.5 * 50) / 15 = 5 hours to catch up to the truck.

Answer 2

5 hours

Explanation:

In order to find out how long it will take the car to catch up to the truck, we can set up a distance equation.

Let's denote the time it takes for the car to catch up to the truck as "t" (in hours).

During this time, the truck has been traveling for (t + 1.5) hours because it left 1.5 hours earlier than the car.

Now, we can calculate the distances traveled by both the car and the truck:

`\sf \textsf{Distance traveled by the car } = \textsf{(car's speed)} * (time)`

Substitute the value:

`\sf \textsf{Distance traveled by the car } = 65* t`

`\sf \textsf{Distance traveled by the car } = 65t miles`

Now,

`\sf \textsf{Distance traveled by the truck = (truck's speed)} * (time)`

Substitute the value:

`\sf \textsf{Distance traveled by the truck }= 50(t + 1.5) miles`

Since the car catches up to the truck, these distances will be equal:

`\sf 65t = 50(t + 1.5)`

Now, we can solve this equation for "t":

`\sf 65t = 50t + 75`

Subtract 50t from both sides:

`\sf 65t -50t = 50t + 75-50t`

`\sf 15t = 75`

Divide both sides by 15 to isolate "t":

`\sf (15t)/(15)=(75)/(15)`

`\sf t = 5`

So, Car will take 5 hours long to catch up to the truck.