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# Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles

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Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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23 May 2016, 11:20
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45% (medium)

Question Stats:

60% (01:44) correct 40% (01:53) wrong based on 107 sessions

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Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?

(A)  3
(B)  3.5
(C)  4
(D)  4.5
(E)  5

Source: Nova's GMAT Math Prep
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Re: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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23 May 2016, 11:56
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DensetsuNo wrote:
Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?

(A)  3
(B)  3.5
(C)  4
(D)  4.5
(E)  5

Source: Nova's GMAT Math Prep

Attachment:

Capture.PNG [ 2.78 KiB | Viewed 1317 times ]

$$\frac{10T}{3}$$ + $$\frac{10T}{3}$$ = $$30$$

So, $$\frac{20T}{3}$$ = $$30$$

Or, T = 4.5

Hence correct answer will be (D)

PS :
DensetsuNo Nova's GMAT Math Prep is a very good source for quants prep ; keep solving and posing more questions...
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Manager
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Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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23 May 2016, 23:14
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Abhishek009 I seldom use Nova's prep, but when I do I'll make sure to post some problems

As for my solution:

We are given the time and the speed at which Fritz runs so we can simply use the $$Distance = Rate*Time$$ formula to find the solution,

$$D1= \frac{1}{3}t * 10mph$$ $$D2= \frac{2}{3}t * 5mph$$, $$D1= \frac{10}{3}t$$, $$D2= \frac{10}{3}t$$,

and since we also know the distance (30 miles) we can simply calculate

$$30 = \frac{10}{3}t + \frac{10}{3}t$$ $$= \frac{20}{3}t$$ -> $$\frac{20}{3}t = 30$$ -> $$t = \frac{90}{20}$$

-> $$t = 4,5h$$

D)
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Re: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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24 May 2016, 05:26
DensetsuNo wrote:
Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?

(A)  3
(B)  3.5
(C)  4
(D)  4.5
(E)  5

Source: Nova's GMAT Math Prep

Let total time= t
F travelled at rate 10mph for t/3 time and 5mph for 2t/3 time

d= s1t1+s2t2
30= 10*t/3 + 5*2t/3
30= 20t/3
t= 4.5

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Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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06 Jun 2016, 18:21
let t=fritz's total time
because his distance for each leg is 10t/3 miles,
we know that each leg=30/2=15 miles
t=(15m/10mph)+(15m/5mph)=4.5 hours
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Re: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles [#permalink]

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27 Sep 2017, 09:50
1
KUDOS
This is a silly question. Why even bother with Mike's stats when they are absolutely worthless in solving this problem?

Given,

Total distance = 30

Assume 'x' to be the total time taken by Fritz to complete the marathon.

For the first $$\frac{1x}{3}$$, the speed is 10. Therefore, the distance (distance= speed x time) traveled in that time is, d1 = $$\frac{10x}{3}$$

For the remaining time $$\frac{2x}{3}$$, the speed is 5. Therefore, the distance (distance= speed x time) traveled in that time is, d2 = $$\frac{10x}{3}$$

The above two distances d1 and d2 sum up to be the total distance of 30

d1+d2 = 30

$$\frac{10x}{3}$$ + $$\frac{10x}{3}$$ = 30

Solving, x = 4.5
Re: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles   [#permalink] 27 Sep 2017, 09:50
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