StudentAidUnit 5: Algebraic Fractions — Exercise 5 5
10th Class Mathematics · Unit 5: Algebraic Fractions
5.5.1.A train travels a distance of 240 km at a uniform rate, if it had finished 4 km an hour slower, it would have taken 2 hours more over the journey. Find its rate of travelling.
Given
Speed
Let speed = x km/h
Formula
Time relation
240x-4 = 240x + 2
240left[1x-4-frac1xright]=2 ⇒ 240 · 4x(x-4)=2 ⇒ x(x-4)=480
x2-4x-480=0 ⇒ (x-24)(x+20)=0
Result
Speed of train
x=24 km/h (rejecting x=-20)
5.5.2.Arshia and Ibraheem complete a job together in 4 hours. If Arshia takes 6 hours, then find how much time will Ibraheem take?
Given
Rates
Arshia's rate=frac16, let Ibraheem's rate=frac1x
Formula
Combined rate
frac16+frac1x=frac14
2x+66x=frac14 ⇒ 4(2x+6)=6x ⇒ 2x=24
Result
x=12 hours
5.5.3.One pipe fills water in 5 hours, another in 8 hours. Second pipe closed after 2 hours. Find the total time.
Given
Rates
Rates: frac15, frac18 part per hour
Work in first 2 hours
left(frac15+frac18right) × 2=1320
Remaining work by pipe 1 alone
1-1320=720;quad 720divfrac15=frac74 hrs
Result
Total time
2+frac74=154=3frac34 hours
5.5.4.Huria can complete a project in 12 hours by working alone. If Abdul Hadi join her and they finish it together in 5 hours, how long would it take Abdul Hadi to do the project alone?
Given
Rates
Huria's rate=frac1{12}, let Abdul Hadi's rate=frac1x
Formula
Combined rate
frac1{12}+frac1x=frac15
x+1212x=frac15 ⇒ 5(x+12)=12x ⇒ 60=7x
Result
x=607=8frac47 hours
5.5.5.Two cars start from opposite towns and head towards each other. The distance between them is 240 km. One travels at x km/h and the other at (x+10) km/h. They meet after 2 hours. Find the speed of each car.
Given
Speeds
Speeds: x, (x+10) km/h
Formula
Sum of distances = total distance
2x+2(x+10)=240
4x+20=240 ⇒ 4x=220
Result
Speeds
x=55; speeds=55 km/h, 65 km/h
5.5.6.Rashid can paint a house in 6 days, but if he gets a helper he can do it in 4 days. How long would it take the helper to paint the house alone?
Given
Rates
Rashid's rate=frac16, let helper's rate=frac1x
Formula
Combined rate
frac16+frac1x=frac14
Multiply by 12x
2x+12=3x
Result
x=12 days