# It takes Maliha two hours more to complete a 50 km journey than it takes ashin to complete a 40 km journey. If the average speed of Maliha for the...journey is 5 km/h less than Ashin, calculate the...

It takes Maliha two hours more to complete a 50 km journey than it takes ashin to complete a 40 km journey. If the average speed of Maliha for the...

journey is 5 km/h less than Ashin, calculate the average speed of each girl by using quadratic equation.

pohnpei397 | Certified Educator

We know that distance = speed*time.  So we can set up equations.

Let Ashin's speed be x.  That means that Maliha's speed is x-5.

So now we know that

40/x = 50/(x-5) - 2

because the time it took Maliha to go 50 km at her speed is 2 hours more than it took Ashin to go 40 km at her speed.

So then what you need to do is multiply both sides by x(x-5)

That will get you

40 (x-5) = 50x -2x(x-5)

Eventually, this will simplify down to

0 = x^2-10x-100

This factors out to (x=6.18)(x-16.18)

Since her speed must be positive, x = 16.18

So Ashin's speed is 16.18 kph and Maliha's speed is 11.18 kph

It took Ashin 2.472 hours to go 40 km and it took Maliha 4.472 hours to go 50 km

neela | Student

Here the speed of the  Mahila and Ahin are to be determined. Let it be x km/h for Mahila.Then , Ashin's speed is x+5 km/h

The time taken by Mahila for 50 kms =50/x ...........(1)

The time taken by Ashin tofor 40 kms = 40(x+5)....(2)

By the condition that Mahila takes 2 hours extra for her 50kms than that of Ashin for 40kms, we get the relation between (1) and (2):

50/x hrs- 40/(x+5) hrs =  2 hrs.......(3). Now solve for x and you get Mahilas speed, and  then x+5 km/h will be Ashin's speed. Multiplying by the x(x+5) both sides of (3):

50(x+5)-40x = 2x(x+5) or

50x+250-40x=2x^2+10x or

10x+250=2x^2+10x  or

2x^2 = 125  or x = (125)^1/2  = 5(5)^(1/2) kms/h is Mahila's speed = 11.18033989 kms/h.

Ashin's speed = x+5 = 5+5(5)^(1/2) kms/h =  16.18033989 kms

Tally:

The time taken by Mahila ans AShin are 50/[5*5^(1/2) = 4.4721... hrs  and 40/{5+5*5^(1/2) = 2.4721... hrs)