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While driving on a highway, Harry and Ron crossed checkpoint

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While driving on a highway, Harry and Ron crossed checkpoint

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Source: e-GMAT

While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

A. 40
B. 60
C. 80
D. 120
E. 160

The OA is D

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BTGmoderatorLU wrote:
Source: e-GMAT

While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

A. 40
B. 60
C. 80
D. 120
E. 160
9am-10am:
Since Harry reaches checkpoint P at 9am -- and travels at rate of 30 mph -- from 9am to 10am Harry travels 30 miles beyond checkpoint P.
Thus, when Ron reaches checkpoint P at 10am, he is 30 miles behind Harry.

Checkpoint Q:
When people compete, SUBTRACT THEIR RATES.
Every hour Ron travels 40 miles, while Harry travels only 30 miles.
Difference between their rates = 40-30 = 10 mph.
Since every hour Ron travels 10 more miles than Harry, every hour Ron catches up to Harry by 10 miles.
Since Ron is 30 miles behind Harry at 10am, and he catches up to Harry at a rate of 10 mph, the time for Ron to catch up to Harry = 30/10 = 3 hours.
Since it takes 3 hours after 10am for Ron to catch up to Harry at checkpoint Q, the time at which Ron catches up to Harry = 10am + 3 hours = 1pm.

1 pm:
Since the professor's rate = 15 mph, the distance traveled by the Professor in the 5 hours between 8am and 1pm = 5*15 = 75 miles.
Thus, at 1pm -- when Ron reaches checkpoint Q and catches up to Harry -- the professor is 75 miles ahead of Ron.
Here, the catch-up rate = (Ron's rate) - (Professor's rate) = 40-15 = 25 mph.
Thus, the time for Ron to catch-up to the Professor = 75/25 = 3 hours.
Since Ron travels beyond checkpoint Q at 40 mph for 3 hours, the distance traveled by Ron after checkpoint Q = 40*3 = 120 miles.

The correct answer is D.

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Solve this question using the concept of relative speed.
Harry left from point P one hour before Ron. In this 1 hr Harry covered 30 km.
To meet Harry at point Q, Ron will have to cover this 30 km relative to Harry.
Relative speed of Ron compared to Harry = 40 - 30 = 10 km / hr
$$So\ Ron\ had\ to\ drive\ for\ \frac{30}{10}\ =\ 3\ hrs\ to\ reach\ meeting\ point\ Q.$$
Means Ron reached at Q at 1 pm.
Now, Snap has been driving from 8 am to 1 pm. So distance covered by him = 15 (speed) * 5 (time) = 75 km
To meet Snap, Ron will have to cover this 75 km relative to Harry.
Relative speed of Ron compared to Snap = 40 - 15 = 25 km / hr
So Ron will drive for 75 / 25 = 3 more hrs to meet Snap.
In 3 hrs, Ron covers distance = 40 * 3 = 120 km , which is his distance from Q.

Ans. D

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BTGmoderatorLU wrote:
Source: e-GMAT

While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

A. 40
B. 60
C. 80
D. 120
E. 160

The OA is D
We see that Harry drove 1 hour more than Ron. If we let t = the number of hours Harry drove, then t - 1 = the number of hours Ron drove, and the distance between points P and Q can be determined by the following equation:

30t = 40(t - 1)

30t = 40t - 40

-10t = -40

t = 4

Therefore, the distance between P and Q is 30(4) = 120 miles. Since Professor Snape left Q at 8 am, he had biked 1 more hour than Harry (or 2 more hours than Ron). In the other words, he had biked 5 hours for 5 x 15 = 75 miles when Harry and Ron arrived at Q at the same time. Thus, Professor Snape had a 75-mile head start over Ron. If we let s = the number of hours it took Ron to catch up with the professor, starting from point Q, we can create the equation:

40s = 15s + 75

25s = 75

s = 3

Since it took Ron 3 hours to catch up with the professor starting from point Q, he had driven 40(3) = 120 miles from point Q.

Answer: D

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scott@targettestprep.com



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