Question

Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister Liz starts from the same location driving at 50 miles per hour. How long after Liz leaves home will she catch up to Candice?

9 hours

4 hours

7 hours

8 hours

Answer 1

The time that Liz will take to catch up with Candice after Liz starts is:

• 4 hours.

Explanation:

We're gonna use the formula:

• Distance = Speed * Time

And we'll give a variable for each driven distance:

• C= Candice's driven distance.

• L= Liz's driven distance.

Now, Liz begins when four hours had passed, then, from the beginning of this exercise Candice's distance is:

• 25 miles / hour * 4 hours = 100 miles

Candice had a 100 miles lead when Liz started, so, the distances 1 hour after Liz began were:

• C= 25 miles / hour * 1 hour + 100 miles = 125 miles.
• L= 50 miles / hour * 1 hour = 50 miles.

When two hours have passed:

• C= 25 miles / hour * 2 hour + 100 miles = 150 miles.
• L= 50 miles / hour * 2 hour = 100 miles.

When three hours have passed:

• C= 25 miles / hour * 3 hour + 100 miles = 175 miles.
• L= 50 miles / hour * 3 hour = 150 miles.

And, when four hours have passed:

• C= 25 miles / hour * 4 hour + 100 miles = 200 miles.
• L= 50 miles / hour * 4 hour = 200 miles.

Then, Liz will catch up with Candice 4 hours after she leaves because after that time the distance traveled is the same for them.