Question

Two trains leave a railway station at the same time. The first train travels due west and the second due north. The first train travels

35 km / hr

faster than the second train. If after two hours, they are

130 km

. apart, find the average speed of each train.

Accepted Answer

Let the speed of the train moving west be $x km / hr .$

So, in $2 hrs$ it travels a distance of $2 x km$ .

Speed of the second train moving towards north is $x - 35 km / hr .$

So, in $2 hrs$ it travels a distance of $2 (x - 35) kms .$

After two hours the position of the two trains along with the starting point makes a right-angled triangle.

Applying Pythagoras theorem in this right-angled triangle we get,

${(2 x)}^{2} + {[2 (x - 35)]}^{2} = 130^{2} \Rightarrow 4 x^{2} + 4 (x^{2} - 70 x + 1225) = 16900 \Rightarrow x^{2} + x^{2} - 70 x - 3000 = 0 \Rightarrow 2 x^{2} - 70 x - 3000 = 0 \Rightarrow x^{2} - 35 x - 1500 = 0$

$\Rightarrow x^{2} - 60 x + 25 x - 1500 = 0 \Rightarrow x (x - 60) + 25 (x - 60) = 0 \Rightarrow (x + 25) (x - 60) = 0 \Rightarrow x + 25 = 0 or x - 60 = 0 \Rightarrow x = - 25, 60$

$x$ being speed cannot be negative. Thus, $x = 60 km / hr .$ .

Therefore, the speed of the train moving west is $60 km / hr$ and speed of the second train moving towards north is $x - 35 = 60 - 35 = 25 km / hr .$

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 5: EXERCISE

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 5: EXERCISE

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Quadratic Equations, Exercise 5: EXERCISE with Hints & Solutions

Learn and Prepare for any exam you want !