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A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey?

1684 km
2600 km
3624 km
4584 km

Answer:- 1

Explanation:-

Solution:

Let the total distance be 2X.

A_____X km_____M_____X km_____B

Total time taken in the journey = 17.5 hours
Time taken to cover X km at 30 km/h = ^X/₃₀.
Time taken to cover X km at 40 km/h = ^X/₄₀
Now,

\begin{aligned} (\frac{X}{30}) + (\frac{X}{40}) = 17.5 \\ [\frac{(40 X + 30 X)}{1200}] = 17.5 \\ 70 X = 17.5 \times 1200 \\ X = 300 k m \\ Total distance, 2 x \\ = 600 k m \end{aligned}

$\eqalign{ & \left( {\frac{X}{{30}}} \right) + \left( {\frac{X}{{40}}} \right) = 17.5 \cr & \left[ {\frac{{\left( {40X + 30X} \right)}}{{1200}}} \right] = 17.5 \cr & 70X = 17.5 \times 1200 \cr & X = 300\,km \cr & {\text{Total}}\,{\text{distance}},\,2x \cr & = 600\,km \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the total distance be 2X.

A_____X km_____M_____X km_____B

Total time taken in the journey = 17.5 hours
Time taken to cover X km at 30 km/h = ^X/₃₀.
Time taken to cover X km at 40 km/h = ^X/₄₀
Now,

\begin{aligned} (\frac{X}{30}) + (\frac{X}{40}) = 17.5 \\ [\frac{(40 X + 30 X)}{1200}] = 17.5 \\ 70 X = 17.5 \times 1200 \\ X = 300 k m \\ Total distance, 2 x \\ = 600 k m \end{aligned}

$\eqalign{ & \left( {\frac{X}{{30}}} \right) + \left( {\frac{X}{{40}}} \right) = 17.5 \cr & \left[ {\frac{{\left( {40X + 30X} \right)}}{{1200}}} \right] = 17.5 \cr & 70X = 17.5 \times 1200 \cr & X = 300\,km \cr & {\text{Total}}\,{\text{distance}},\,2x \cr & = 600\,km \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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