Question

Two electric train leaves railway station at the same time the first train travels due West and the second train travels due north the first train travel 5 kilometre per hour faster than the second train if after an hour they are 25 kilometre apart then the speed of first train is what ​

Answer 1

Let s = the speed of the northbound train

Then

(s+5) = the speed of the westbound train

:

This is a right triangle problem: a^2 + b^2 = c^2

The distance between the trains is the hypotenuse

dist = speed * time

The time is 2 hrs, so we have

a = 2s; northbound train distance

b = 2(s+5) = (2s+10); westbound distance

c = 50; distance between the two trains

:

(2s)^2 + (2s+10)^2 = 50^2

4s^2 + 4s^2 + 40s + 100 = 2500

 Arrange as a quadratic equation4s^2 + 4s^2 + 40s + 100 - 2500 = 0

8s^2 + 40s - 2400 = 0

:

Simplify, divide by 8:

s^2 + 5s - 300 = 0

:

Factors to

(s - 15)(s + 20) = 0

:

The positive solution is what we want here

s = 15 mph is the speed of the northbound train

then

5 + 15 = 20 mph is the speed of the westbound train

:

:

Check this; find the distance (d) between the trains using these distances

Northbound traveled 2(15) = 30 mi

Westbound traveled 2(20) = 40 mi

d = 

d = 50