got Mike total time = 10/10+20/5 ; 5 hrs
for Fritz total time =
30= t/3 *10+2t/3*5
solve for t= 90/20 ; 4.5 hrs
IMO D

distance =velocity*time
1/3*t*10+2/3*t*5=30
10t/3+10t/3=30
20t=3*30
t=4.5
ans :D

Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles
why is this information provided in the question?

Ballparking choices one by one

Let’s take 3 hours

Then 10 miles in 1 hr and 2 hr x5 = 10 so incorrect

Then take some thing which can be divided by 3

So 4.5

Bingo 1.5 hour x 10 miles/hr = 15 miles
And remaining 3 hour x 5 = 15

D is correct

Posted from my mobile device

Hi prgmatbiz,

IMO this information is absolutely redundant and not useful. I believe it has been given only to confuse the test taker. This is so because there is just no relationship between these two people. The test taker must have an eye to spot what is useful and what is not to answer this question. I have rarely come across official questions that give information that is absolutely useless, but this doesn't mean this can't happen!
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Solution:

Let t be the total amount of time it took Fritz to complete the Marathon. Then, Fritz ran for t/3 hours at 10 mph and 2t/3 hours at 5 mph. Since distance = rate x time, Frits ran a total of 10 * t/3 + 5 * 2t/3 = 10t/3 + 10t/3 = 20t/3 miles. We are told that the total distance is 30 miles, so let’s set the expression 20t/3 equal to 30:

20t/3 = 30

2t = 9

t = 4.5 hours

Notice that since we already know the total distance is 30 miles, the given information about Mike is completely unnecessary.

Answer: D
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