Question

Two brothers leave from the same point driving in opposite​ directions, the first brother driving at 55 miles per hour and the second at 50 mph. The first brother has a​ one-hour head start. If each brother has a communication device that allows him to talk to the other for up to a 210​-mile ​range, how long will they be able to talk to each​ other?

Answer 1

Answer: they would be able to talk to each other for 1.5 hours

Step-by-step explanation:

If each brother has a communication device that allows him to talk to the other for up to a 210​-mile ​range, by the time they are 210 miles apart, they won't be able to communicate to each other. This means that they would have travelled a total distance of 210 miles.

Let t represent the time it takes either brothers to travel his own distance.

the first brother driving at 55 miles per hour. If the first brother has a​ one-hour head start, this means that the time spent by the first brother is (t + 1) hour.

Distance = speed × time

Distance travelled by the first brother is

55(t + 1) = 55t + 55

The second brother was driving at 55 miles per hour. This means that distance travelled by the second brother in t hours is

50t

Since the total distance covered is 210 miles, then

55t + 55 + 50t = 210

105t = 210 - 55 = 155

t = 155/105 = 1.476 hours

Approximately 1.5 hours