Question

two trains leave se railway station at the same time first time travel towards west and the second and travels towards north the first time is 10 kilometre faster than the second if after 3 hours there are 150 km apart find the average speed of each train​

Answer 1

Answer:

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