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Jonah drove the first half of a 100-mile trip in x hours and

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by BTGmoderatorLU » Sat Oct 27, 2018 2:14 pm
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Source: Official Guide

Jonah drove the first half of a 100-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip?

A. 50/(x + y)
B. 100/(x + y)
C. 25/x + 25/y
D. 50/x + 50/y
E. 100/x + 100/y

The OA is B.
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by deloitte247 » Sun Oct 28, 2018 8:08 am
Time taken by jonah to cover first half that is the 50km
50km of 100mile trip = x
Time taken by jonah to cover the second half which is another 50km of a 100mile =y
Total time taken = x+y
$$Average\ speed=\frac{dis\tan ce}{time}$$
Jonah's average speed for the entire trip= $$\frac{dis\tan ce}{time}$$= $$\frac{100}{x+y}$$
$$answer=option\ B$$
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by fskilnik@GMATH » Sun Oct 28, 2018 12:35 pm
BTGmoderatorLU wrote:Source: Official Guide

Jonah drove the first half of a 100-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip?

A. 50/(x + y)
B. 100/(x + y)
C. 25/x + 25/y
D. 50/x + 50/y
E. 100/x + 100/y
\[?\,\,\,\, = \,\,\,\frac{{\,{\text{total}}\,\,{\text{# }}\,\,{\text{miles}}\,}}{{{\text{total}}\,\,{\text{# }}\,\,{\text{hours}}}}\,\,\, = \,\,\,\frac{{100}}{{x + y}}\,\,\,\,\,\,\,\left[ {\,{\text{mph}}\,} \right]\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Sun Oct 28, 2018 7:15 pm
Hi All,

We're told that Jonah drove the first half of a 100-mile trip in X hours and the second half in Y hours. We're asked which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip. This question can be solved in a couple of different ways, including by TESTing VALUES.

Since we're dealing with the trip in two 50-mile pieces, we should TEST values for X and Y that divide evenly into 50. Let's TEST X=5 and Y=10
The first 50 miles were traveled in 5 hours.
The second 50 miles were traveled in 10 hours.
Total Distance = 100 miles and Total Time = 15 hours

Total Dist = (Av. Sp.)(Total Time)
100 miles = (Av. Sp)(15 hours)
100/15 = Av. Sp. = 6 2/3 miles/hour

Based on the design of the answer choices, we don't actually have to do that last extra calculation. Only one of the answers will equal 100/15 when you TEST X=5 and Y=10....

Final Answer: B

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Rich
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