# Solving Linear Equations Word Problems Worksheet

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It goes 30 km upstream and 21 km downstream in 6 hrs and 30 min.

Find the speed of the boat in still water and also speed of the stream.

A's father D is twice as old as A and B is twice as old as his sister C. Five years ago, father was seven times as old as his son. Hint: $(x 5)=3 (y 5)$ $(x-5) =7(y-5)$ Answer 40 year, 10 year Question 5 The ages of two friends Manjit and Ranjit differ by 3 years.

Hint: $\frac x \frac y =2000$ $\frac x - \frac y = 1500$ Answer (20,000, 10,000) Question 3 A and B are friends and their ages differ by 2 years. Hint: $x - y =2$ $2x - \frac = 40$ x=26 and y=24 Question 4 Five years hence, father's age will be three times the age of his son.

Just as "26" is "10 times 2, plus 6 times 1", so also the two-digit number they've given me will be ten times the "tens" digit, plus one times the "units" digit.

In other words: that make the quadratic equation true.If he walks 1/2 km an hour faster, he takes 1 hour less.But, if he walks 1 km an hour slower, he takes 3 more hours.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.All of these different permutations of the above example work the same way: Take the general equation for the curve, plug in the given points, and solve the resulting system of equations for the values of the coefficients.Simply put, two-step equations – word problems are two step equations expressed using words instead of just numbers and mathematical symbols.Plugging the three points in the general equation for a quadratic, I get a system of three equations, where the variables stand for the unknown coefficients of that quadratic: ..other conics, though parabolas are the most common.Keep in mind that projectile problems (like shooting an arrow up in the air or dropping a penny from the roof of a tall building) are also parabola problems, using: if you're working in feet).Hint: Let speed of boat in still water be x km/h and speed of stream be y km/h.Speed upstream= (x - y) km/h Speed downstream= (x y) km/h $\frac \frac = 10$ $\frac \frac = 13$ Now Substituting $p=\frac$ and $q=\frac$,then solving p=1/5 and q=1/11 Hence $x-y=5$ and $x y =11$, Solving these, x=8 km/hr and y=3km/hr Question 8 A boat goes 24 km upstream and 28 km downstream in 6 hrs.

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