Fanny and Alexander are y miles apart and are traveling in a straight

Hi,

Given,

Speed of fanny = 25mph

Speed of alexander = “x” mph

Distance between them = “y” miles

Since both of them travelling towards each other (opposite directions), relative speed is sum of their speeds.

i.e., Every hour both will cover = (25+x) mph

Question: Speed of alexander = “x” mph ?

Statement I is sufficient:

1.5 hours before they meet they were 135 miles apart.

This tells the remaining time taken and the distance to cover.

i.e., both will travel 135 miles in 1.5 hours.

So, time = distance/ Speed

1.5 = 135/(25+x)

We can stop here, clearly there will be one value of “x”.

37.5 + 1.5x = 135.

x = 97.5/1.5

x = 65.

So sufficient.

Statement II is insufficient:

y = 360 miles.

Knowing only the distance doesn’t help here. We need to know the time.

So insufficient.

So the answer is A.

Hope this helps.

Regards,
Junaid.
Byjus GMAT Quant Expert

Statement 1: Relative speed = (25+x) mph. Distance covered = 135 in 1.5 hrs. Hence, 135/(25+x)=1.5, x=65. Sufficient.

Statement 2: Relative speed = (25+x) mph. y = 360 miles but no information on time taken to meet each other. Insufficient.

Option: A

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

Given: Fanny and Alexander are y miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and x mph respectively.

Asked: What is the value of x?

(1) 1.5 hours before they meet they were 135 miles apart
Relative speed = 135/1.5 = 90 mph = 25 + x
x = 65 mph
SUFFICIENT

(2) y = 360 miles
NOT SUFFICIENT

IMO A

Answer: alternative A


Explanation:


Since it is an example of a meeting, in opposite directions (one advances towards the other), the hour and a half remaining until the meeting between Fanny and Alexander must be traveled by both with their respective speeds and then you must add them.

ie) 65 x 3/2 + 25 x 3/2 = (65 + 25) x 3/2 = 90 x 3/2 = 135 miles.