Ravi travels 800 km/h partly by train partly by car. he takes 17 hours to travel 600 km by train and rest by car . he takes 12 minute more if he travels 560 km by train and the rest by car . determine the speed of the car and of the train

Step-by-step explanation:

Let t and c represent the speeds of the train and car (in km/h), respectively. The applicable relationship is ...

  time = distance/speed

so we have fir the first trip ...

  600/t + 200/c = 17

and for the second trip ...

  560/t +240/c = 17.2 . . . . . . 17 hours + 12 minutes = 17.2 hours

These equations can be fairly easily solved using Cramer's rule*:

  t = (200·560 -240·600)/(200·17.2 -240·17) = -32000/-640 = 50

  c = -32000/(17·560 -17.2·600) = -32000/-800 = 40

The speed of the train is 50 km/h; the speed of the car is 40 km/h.

* Cramer's rule ordinarily gives a ratio for the variables x=1/t and y=1/c. By inverting that ratio, we can find the values of t and c.

The applicable "Cramer's rule" for ...

is ...

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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