average speed

Ankitaverma wrote:A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph[/b]

Dear Ankitaverma
I'm happy to help. Here's a blog on distance, rate, and time:
https://magoosh.com/gmat/2012/gmat-math-rate-questions/

For this question --- Day #2, hiker walks for 2 hours more than the first day, for a total of 18 hours of walking. That means 8 hr of walking the first day, and 10 hours of walking the second day. I think backsolving is much easier and more efficient than an algebraic approach
https://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/
Starting with (C)
If he walks 4 mph for 8 hours on Day 1 = 32 mi
Then 5 mph for 10 hours on Day 2 = 50 mi
Total = 32 + 50 = 82
Too much distance. Choices (C) & (D) & (E) are incorrect.

Try (B).
Day 1: 3 mph for 8 hours = 24 mi
Day 2: 4 mph for 10 hours = 40 mi
Total = 64 mi.
That's it! Answer = (B).

Does all this make sense?
Mike

Hi Ankitaverma,

These types of questions are usually easier to handle if you create a table to organize your information, although you're going to have to do some algebra no matter how you organize.

We're told about 2 days (Day 2 was 2 hours longer and at a speed that was 1 mph more than Day 1). The information implies that we'll use the Distance Formula:

Distance = Rate x Time

Day 1: D = R x T
Day 2: D = (R+1) x (T+2)

Then we're told that the TOTAL Distance = 64 miles and the TOTAL Time was 18 hours.

Since the 2 "times" add up to 18 hours, we know:

T + (T+2) = 18
2T = 16
T = 8
This gives us:

Day 1: D = R x 8
Day 2: D = (R+1) x 10

We know the total distance is sum of the two "distances":

64 miles = 8R + 10(R+1)
64 = 8R + 10R + 10
54 = 18R
3 = R

The question asks us for the rate on Day 1 (so, what is R?)

Final Answer: [spoiler]B: 3[/spoiler]

GMAT assassins aren't born, they're made,
Rich