Average Speed Question

[mrozelle5900]

Hi all,

Andrea makes a certain trip in her car. On the first leg she drives 40 miles per hour to her destination. On the second leg she turns and around and drives the same route in 4 hours. How long did she spend driving on the first leg?

1) The average speed for the trip is 35 miles per hour
2) The distance to her destination is 110 miles

I am told that both of these answers are sufficient on their own to find the answer. However, I am not sure how.

Looking for any and all help I can receive. Thank you

 

[Ishuda]

Hi all,

Andrea makes a certain trip in her car. On the first leg she drives 40 miles per hour to her destination. On the second leg she turns and around and drives the same route in 4 hours. How long did she spend driving on the first leg?

1) The average speed for the trip is 35 miles per hour
2) The distance to her destination is 110 miles

I am told that both of these answers are sufficient on their own to find the answer. However, I am not sure how.

Looking for any and all help I can receive. Thank you

What I think you mean is that either (1) or (2) is sufficient, not that both (1) and (2) are needed.

Given
s1 = 40 mph
t2 = 4 hrs
s1 t1 = D
s2 t2 = D
where s1 and s2 are the average speed and t1 and t2 are the time taken on the first & second leg respectively and D is the total distance of one leg.

(1) says
2 D = 35 (t1 + t2) = 35 (t1 + 4) = 35 t1 + 140
=> 2 s1 t1 = 2 * 40 t1 = 35 t1 + 140
=> t1 = (28/9) hrs, D = (1120/9) miles, and s2 = (280/9) mph

(2) can be done in a similar manner and, in fact, as Denis pointed out, the actual answer to your question is available directly.