Difficult Math Question #54 - Rates

[800guy]

Two people walked the same distance, one person's speed is between 25 and 45,and if he used 4 hours, the speed of another people is between 45 and 60,and if he used 2 hours, how long is the distance?

A.116
B.118
C.124
D.136
E.140

[kulksnikhil]

Two people walked the same distance, one person's speed is between 25 and 45,and if he used 4 hours, the speed of another people is between 45 and 60,and if he used 2 hours, how long is the distance?

A.116
B.118
C.124
D.136
E.140

A and B both are satisfying the ranges (25~45 and 45~60) :roll:

[800guy]

here's the suggested OA:

First person-- speed is between 25mph and 45mph
so for 4 hrs he can travel 100 miles if he goes at 25mph speed
and for 4 hrs he can travel 130 miles if he goes at 45 mph speed

similarly

Second person-- speed is between 45mph and 60mph
so for 2 hrs he can travel 90 miles if he goes at 45mph speed
and for 2 hrs he can travel 120 miles if he goes at 60 mph speed

So for the first person---distance traveled is greater than 100 and Less than 130

and for the second person---distance traveled is greater than 90 and less than 120

so seeing these conditions we can eliminate C, D, and E answers...

but I didn’t understand how to select between 116 and 118 as both these values are satisfying the conditions...

[800guy]

yeah this was a poorly written question

[hishighness]

See the main logic is they both have to cover the same distance and one should take take half the time taken by other persson .. which means speed of one should be double the speed of other person Between 25-45 and 45-60 double speed combos can be

25,50
26,52
27,54
28,56
29,58
30,60

Now see the choices --- Only 116 is in choice
100,104,108,112,120 are not in choices

[800guy]

See the main logic is they both have to cover the same distance and one should take take half the time taken by other persson .. which means speed of one should be double the speed of other person Between 25-45 and 45-60 double speed combos can be

25,50
26,52
27,54
28,56
29,58
30,60

Now see the choices --- Only 116 is in choice
100,104,108,112,120 are not in choices

thanks for the clarification!!

[Stuart@KaplanGMAT]

See the main logic is they both have to cover the same distance and one should take take half the time taken by other persson .. which means speed of one should be double the speed of other person Between 25-45 and 45-60 double speed combos can be

25,50
26,52
27,54
28,56
29,58
30,60

Now see the choices --- Only 116 is in choice
100,104,108,112,120 are not in choices

To dredge up old wounds (since someone reposted) - nowhere does it say the rates have to be integers!