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Jake rides his bike for the first 2/3 of the distance from home to sch

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Re: Jake rides his bike for the first 2/3 of the distance from home to sch [#permalink]

Solution

Given:
• Jake rides his bike for the first $$\frac{2}{3}$$ of the distance from home to school at 10 mph
• He walks the remaining $$\frac{1}{3}$$ distance at 3 mph
• Total travel time is 40 minutes or $$\frac{2}{3}$$ hours

To find:
• The distance between Jake’s home to his school

Approach and Working:

If we assume the total distance to be x miles, we can write
• Distance travelled in bike = $$\frac{2x}{3}$$ miles
• Therefore, time for bike travel = ($$\frac{2x}{3}$$/10) hours = $$\frac{x}{15}$$ hours
• Distance travelled in walk = $$\frac{x}{3}$$ miles
• Therefore, time for walk = ($$\frac{x}{3}$$/3) hours = $$\frac{x}{9}$$ hours

As the total travel time is $$\frac{2}{3}$$ hours,
• $$\frac{x}{15} + \frac{x}{9}$$ = $$\frac{2}{3}$$
Or, $$\frac{8x}{45}$$ = $$\frac{2}{3}$$
Or, x = $$\frac{90}{24}$$ = $$\frac{15}{4}$$ miles

Hence, the correct answer is option B.

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Re: Jake rides his bike for the first 2/3 of the distance from home to sch [#permalink]
Answer is B for the explanations given above.
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Re: Jake rides his bike for the first 2/3 of the distance from home to sch [#permalink]
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Bunuel wrote:
Jake rides his bike for the first 2/3 of the distance from home to school, traveling at 10 miles per hour. He then walks the remaining 1/3 of the distance at 3 miles per hour. If his total trip takes 40 minutes, how many miles is it from Jake's home to his school?

A. $$\frac{5}{4}$$

B. $$\frac{15}{4}$$

C. 5

D. 6

E. 10

We can let d = the distance from Jake’s home to his school. Thus,

The time spent riding the bike is (2d/3)/10 = 2d/30 = d/15.

The time spent walking is (1d/3)/3 = d/9.

Since 40 minutes = 2/3 of an hour, we can create the equation for time:

d/15 + d/9 = 2/3

3d/45 + 5d/45 = 2/3

8d/45 = 2/3

24d = 90

d = 90/24 = 30/8 = 15/4 miles.

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Re: Jake rides his bike for the first 2/3 of the distance from home to sch [#permalink]
in the question they have said that "He then walks the remaining 1/3 of the distance" shouldnt the remaining 1/3rd distance be (1/3)*(2/3)*(x) as he has already covered (2/3)*(x) on his bike so the remaining should be 1/3rd of (2/3)*(x) ?

if that is not the case then when should we take (1/3)*(2/3)*(x)
like how should we know when something like this "(1/3)*(2/3)*(x)" should be considered
Re: Jake rides his bike for the first 2/3 of the distance from home to sch [#permalink]
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