John travels from A to B, which are 60 miles apart, at 11 mph starting

Question

John travels from A to B, which are 60 miles apart, at 11 mph starting at 11 a.m. His sister leaves B for A at 1:00 p.m. at 8 mph. When do they meet?

A. 2:00 p.m.
B. 2:30 p.m.
C. 2:45 p.m.
D. 3:00 p.m.
E. 4:00 p.m.

LevanKhukhunashvili · Answer

When the sister begins to travel, the distance between the siblings is 60-22=38, as John has already covered 22m
After that, if t is the time before they meet, we have got an equation
11t+8t=38
t=2

IMO
Ans:  D

Archit3110 · Answer

distance travelled by john till 1 pm ; 2hrs is 11*2 ; 22 miles
so total distance to be covered b/w a & b ; 60-22; 38 miles
now
since they are in opposite direction so relative speed; 11+8 ; 19 mph
time they will meet ; 38/19 ; 2 hrs from 1 pm
i.e 3 pm
IMO D

Diya52 · Answer

Let t be the time taken by John's sister to travel. John starts at 11am so he gets 2hrs more travel time. Therefore john's travel time is t+2 hrs. The distance travelled by john to the meeting point and the distance travelled by john's sister to the meeting point must equal the total distance travelled. So we can set up the equation as 11(t+2)+8t=60
Or 19t=38. Or t=2hrs. Since we took t as the time taken by john's sister. The time when they meet is 1pm+2hrs=3PM. Answer D

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ScottTargetTestPrep · Answer

We can let John’s sister’s time = t and thus John’s time = t + 2.

Thus, John’s distance is 11(t + 2) = 11t + 22 and his sister’s distance is 8t. Thus:

11t + 22 + 8t = 60

19t = 38

t = 2

So they will meet at 3 pm.

Alternate Solution:

At 1:00pm, John has already traveled for 2 hours, and since he is traveling at 11 mph, he has traveled 22 miles. Thus, at 1:00pm, the distance between John and his sister is 60 - 22 = 38 miles.

Since John and his sister are traveling towards each other, the distance between the two is decreasing by 11 + 8 = 19 miles every hour. Since the distance is 38 miles at 1:00pm, it will take 38/19 = 2 hours for the distance to become zero; i.e. they meet. Thus, the two will meet at 1:00pm + 2 hours = 3:00pm.

Answer: D

bumpbot · Answer

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John travels from A to B, which are 60 miles apart, at 11 mph starting

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