# Solving Word Problems Using Equations

To simplify this equation, multiply both sides by , then transfer all terms from the right side to the left with the opposite signs, collect the common terms and adjust the signs. Solution Let be number of hours to fill the reservoir using the smaller tube only.Then is the time in hours to fill the reservoir using the larger tube only.

A motorboat makes a round trip on a river 56 miles upstream and 56 miles downstream, maintaining the constant speed 15 miles per hour relative to the water. When motorboat moves upstream, its speed relative to the bank of the river is miles/hour, and the time spent moving upstream is hours. For more examples of solved word problems of this type see the lesson Wind and Current problems solvable by quadratic equations under the topic Travel and Distance of the section Word problems in this site.In this case, it would be the hours that we had to work to earn that wage.We will mark it using the letter „X“ (you can use whatever letter you want).Working together, Andrew and Bill make of the whole work in each single day. The second root does not fit the given conditions: if Bill covers the roof in two days, then Andrew has 2-5=-3 days, which has no sense. The larger tube, if works separately, can fill the reservoir in 18 hours faster than the smaller tube.Since they can cover the entire roof in 6 days working together, the equation for the unknown value is as follows: . Apply the quadratic formula (see the lesson Introduction into Quadratic Equations) to solve this equation. So, the potentially correct solution is : Bill covers the roof in 15 days. If Bill gets the job done in 15 days, then Andrew makes it in 10 days, working separately. How long will it take to fill the reservoir using the smaller tube only?When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ... and a Quadratic Equation tells you its position at all times! There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics: a×c = A very profitable venture.Your company is going to make frames as part of a new product they are launching.50 * X = 400 Your hourly wage is on the left side with the variable because you have to work „X“ hours a day while being paid 50\$ per hour to earn your daily wage of 400\$ (which is on the right side of the equation).Since this is a one-step equation, the only thing left to do is to get rid of the number in front of our variable so we can find the value of „X“.How many hours did you have to work to earn that kind of money?The first thing we have to do is to recognize the variable.

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