+0

# Highway Question (Will help me in a competition tomorrow)

0
412
4
+2854

Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming the buses travel on the same highway, how many Dallas-bound buses do a Houston-bound bus pass on the highway (not in the station)?

Jan 11, 2019

#1
+533
0

while a houston bus is traveling, it takes 5 hours, and since the dallas buses leave every hour on the half hour, the answer is 5/(1/2) or 10.

HOPE THIS HELPED!!

Jan 12, 2019
#2
+2854
+2

Thank You!!!

It took me much longer than it needed to solve this problem, thank you for this solution

Jan 12, 2019
edited by CalculatorUser  Jan 12, 2019
#3
+111328
+1

This is a little trickier than it seems......let us assume that all the buses travel at the same speed

Let us suppose that a bus leaves Dallas at the same time  that a bus arrives from Houston...we don't count that one

Notice that, at that point.....there is another Dalllas-bound bus that is 30min from Dallas

But....since the buses travel at the same speed, and they travel towards each other,  they will actually  meet  15 min after the bus bound for Houston leaves Dallas

Then, when these buses meet, there is another bus bound for Dallas that is 30min from the Houston- bound bus....but they will again meet in another 15 min because they are traveling towards each other

So....following this pattern, the Houston- bound bus will meet a Dallas-bound bus every 15 min

Notice that  the Houston-bound bus will meet the last Dallas-bound bus 4 hrs, 45 min into its trip

At this point it will have met 19 Dallas-bound buses

And in another 15 min....it wiil arrive at the Houston station at the top of the hour and not pass any more buses

So...it will pass 19 Dallas-bound buses on the way.....

Jan 12, 2019
edited by CPhill  Jan 12, 2019
edited by CPhill  Jan 12, 2019
edited by CPhill  Jan 12, 2019
edited by CPhill  Jan 12, 2019
#4
+2854
+2

Thanks!

Jan 21, 2019