# Solving Linear Equations Word Problems Worksheet Hint: This question is exactly same as above question 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 $\frac \frac = 6$ $\frac \frac = 6.5$ Now Substituting $p=\frac$ and $q=\frac$,then solving p=1/6 and q=1/14 Hence $x-y=6$ and $x y =14$, Solving these, x=10 km/hr and y=4km/hr Question 9 A man walks a certain distance with certain speed.It goes 30 km upstream and 21 km downstream in 6 hrs and 30 min.

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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.

It can go 16 km upstream and 32 km downstream in the same time.

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

Many problems lend themselves to being solved with systems of linear equations.

In "real life", these problems can be incredibly complex.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.We will do that by dividing the whole equation by 4.4 * x = 20 |:4 x = 5 Now that we have calculated the value of the variable, we can tell that Janice rented that bike for 5 hours. If you multiply that Janice paid per hour by the 5 hours she spend with that bike and then add the she had to pay regardless of the time she spent with the bike, you will get a total sum of that is indeed the full sum she paid.This is one reason why linear algebra (the study of linear systems and related concepts) is its own branch of mathematics.In your studies, however, you will generally be faced with much simpler problems. The ten's digit stands for "ten times of this digit's value".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).They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve.If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. First thing we have to do in this assignment is to find the variable and see what its connection is with the other values. 4 * x 10 = 30 Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation.

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