tough distance problem

jsasipriya wrote:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A 48
B 72
C 96
D 120
E 192

OA E

Can someone help me?

d -> distance between cities

First meeting point -> d/2 (both buses travel at the same constant speed and leave the cities same time)

Total time to cover d -> 4 hours (Since both bus travel at same speed and for 2 hrs each)

On the second day first bus traveled alone 1 hour (36mins +24mins = 60 mins), hence covered d/4.

Leftover distance = d - d/4 = 3d/4

Again since the speed of both the buses is same, they will meet at halfway of 3d/4, which is 24 miles from d/2:

d/2-24 = 3d/8

=> d = 192

Hence , E

IMO E

let speed of each bus = v
distance = d

bus2---------------------------*---------------------------bus1
bus2------------------*------------------------------------bus1

Suppose * denotes the meeting point of buses.
this separation is 24 miles.
bus1 started 1 hour (24+36 mins) earlier than bus2


& distance_bus1 + distance_bus2 = d

2hrs * v + 2hrs * v = 1 hr *v + t *2v

t=1.5

so separation between the two meeting points = [1 hr*v +t *v ] - 2hr *v = 24 miles
t=0 when bus2 starts

v=48 mph

d = 4 *v = 192 miles

jsasipriya wrote:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A 48
B 72
C 96
D 120
E 192

OA E

Can someone help me?

Thanks!

Since on the first day each bus travels for 2 hours, the total time to cover the distance between the two cities is 2+2 = 4 hours.

On the return trip, one bus leaves 36 minutes earlier and the other bus leaves 24 minutes later. Thus, the earlier bus will travel 36+24 = 60 minutes = 1 hour longer than than the later bus. Since the total travel time to cover the distance must remain 4 hours, the earlier bus will travel for 2.5 hours and the later bus will travel for 1.5 hours.

Since the earlier bus travels for 2 hours on the first day and 2.5 hours on the return trip, the earlier bus travels for 1/2 hour more on the return trip. Since the meeting point on the return trip is 24 miles from the meeting point on the first day, during its 1/2 hour of extra travel time the earlier bus has to travel 24 more miles than it did on the first day.

Now we can plug in the answer choices, which represent the distance between the 2 cities. On the first day, the earlier bus will travel 1/2 the distance, since the two buses are traveling toward each other at the same rate. On the return trip, the earlier bus must travel 24 more miles during its 1/2 hour of extra travel time.

Answer choice C: 96 miles between the 2 cities
Distance traveled by the earlier bus on the first day = 1/2*96 = 48 miles.
Rate of the earlier bus = d/t = 48/2 = 24 miles per hour.
On the return trip, the earlier bus will travel r*t = 24*(1/2) = 12 more miles.

The distance needs to be doubled. Since 2*96 = 192, the correct answer is E.

to: anshumishra

How do you know the two buses meet half way through?

trangle wrote:to: anshumishra

How do you know the two buses meet half way through?

Because both are travelling towards each other and with same speed.