Name: Solving Free Fall Problem Using Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 7 s
Description: In this video, we will learn how we can solve the problem of free fall effectively using the quadratic equation. Let's watch the video and learn.

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 $x - 35 = 60 - 35 = 25 km / hr .$

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.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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.