Question

Some friends are leaving a party in Princeton to go home. One group takes a taxi uptown, traveling north at 34 miles per hour. The rest of the friends share another taxi, traveling south at 42 miles per hour. If the two taxis depart at the same time, how much time will pass before they are 10 miles apart?

Answer 1

To find the time it takes for the two taxis to be 10 miles apart, we can use the concept of relative speed. The taxis are moving in opposite directions, so their relative speed is the sum of their individual speeds. The northbound taxi is traveling at 34 miles per hour, while the southbound taxi is traveling at 42 miles per hour. Therefore, their combined speed is 34 + 42 = 76 miles per hour.

We can use the formula time = distance / speed to calculate the time it takes for them to be 10 miles apart. Plugging in the values, we have time = 10 miles / 76 miles per hour ≈ 0.13 hours.

Therefore, it will take approximately 0.13 hours, or about 7.89 minutes, for the two taxis to be 10 miles apart.