Another approach...


GIVEN: It took Ellen 6 hours to ride her bike a total distance of 120 miles.

Let d = the distance traveled at 25 miles per hour
So, 120 - d = the distance traveled at 15 miles per hour

Now let's start with the word equation:
( time spent travelling at 25 miles per hour) + ( time spent travelling at 15 miles per hour) = 6 hours

time = (distance)/(speed)

We get: d/25 + (120 - d)/15 = 6 hours
To eliminate the fractions we'll multiply both sides of the equation by 75 (the least common multiple of 25 and 15)
We get: 3d + 600 - 5d = 450
Simplify: 600 - 2d = 450
Subtract 600 from both sides to get: -2d = -150
Solve: d = 75

So, Helen traveled at 25 mph for 75 miles

Answer: D

Cheers,
Brent

25x + 15x = 120
or, 40x = 120
or, x = 3
so that in the first trip 25*3 = 75 miles
and in the second trip 15*3 = 45 miles
total 120 miles.
thank you

@Asif123

Why are you assuming that the distance traveled with 25 mph speed and 15 mph speed are equal?

i have different approach always to such questions, including ratios as well.
i use distance method. its much simple and straight forward.
distance is 120, covered in 6 hours. so average rate is 20.


now draw a line

15 20 25
each has a distance(difference) of 5 from 20. so it means that the proportion of time is same for both speeds. in this regard, 6*1/2=3
so distance covered at speed 25=25*3 =75
so ans is 75

d/15+(120-d)/25=6, where d= distance at rate 15 m/h.
solving, d=45.
we need, 120-45=75.

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