# Solving Linear Equations Word Problems Worksheet A says to B, “if you give me 10 of your apples, I will have twice the number ofapples left with you”. In 13 hours, it can go 40 km upstream and 55 km downstream.B replies, “if you give me 10 of your apples, I will the same number ofapples as left with you.” Find the number ofapples with P and Q separately Hint: $x 10 =2(y-10)$ $x-10 = y 10$ Answer (70, 50) Question 2 On selling a T. at 5% gain and a fridge at 10% gain, Reliance digitalgains Rs 2000. Determine the speed of stream and that of the boat in still water.Find the distance covered by the man and his original rate of walking.Hint: Let v = the rate the man walked, t=time taken originally and d=distance $d=vt$ Case 1 (faster) Speed= (v .5) time=(t-1) = time taken at the faster speed Now $distance = velocity \times time$ $vt= (v .5)(t-1)$ $v - .5t = -.5$ (1) Case 2 (slower) speed=(v-1) time=(t 3) Now $distance = velocity \times time$ $vt = (v-1)(t 3)$ $-3v t = -3$ (2) Solving (1) and (2) v=4 km/hr ,t=9 hr, hence d= 36 km Question 10 Anuj travels 600 km partly by train and partly by car.To practice solving two-step equations – word problems, feel free to use the worksheets below.Question 1 P and Q each have certain number of apples. But if A doubles his pace, he is ahead of B by one and half hrs. Hint: Let x and y be the speed of A and B $\frac - \frac = 3$ $\frac - = \frac$ Now Substituting p=1/x and q=1/y,then solving p=3/10 and q=1/5 So x=3.3 km/hr and y=5 km/hr Question 7 The boat goes 30 km upstream and 44 km downstream in 10 hours.

But, if he walks 1 km an hour slower, he takes 3 more hours.

These word problems are called two-step because you have to perform two mathematical operations in order to solve them.

In this case – addition (subtraction) and multiplication (division).

If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes.

But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Hint: Let x and y be the speed of train and car,then using time= distance/speed $\frac \frac = 6.5$ $\frac \frac = 7$ Now Substituting $p=\frac$ and $q=\frac$,then solving 0p 200q=6.5$0p 400 q=5$ p=1/100 and q=1/80 hence x=100 km/hr and y=80km/hr Question 11 A boat goes 12 km upstream and 40 km downstream in 8 hours.

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