Question

Tania, a long distance runner, runs at an average speed of 5 mph. Five hours after tanning leaves your house, you leave in your car and follow the same route. If your average speed is 55 mph, how long will it be before you catch up the Tania? How far will each of you be from your home?

Answer 1

a) 1/2 hour = 30 minutes after car leaves to catch up with Tania.

b) 27.5 miles will be the catch up distance point.

Explanation:

Step 1

Set the equation to = each other.

ie) your car distance = Tania's running distance

55t = 5(t+5)

55t = 5t + 25

55t - 5t = 25

50t = 25

t = 25 / 50

t = 1/2

t = 1/2 = 1/2 hr = 30 minutes additional catch up time.

Step 2.

Find the distance using = 0.5 hr for additional time and checking Tania's 5.5 hr for Distance as checking multiples to match.

50 * 0.55 = 27.5 miles

5 * 5.5 = 27.5 miles

Answer 2

It would take me Approximately 55 minutes to catch up with her and we would be 50 miles from my home