Word problems and liner equations

[caprija]

Can someone please help me with this question?

Kareem took 5 h to drive 470km from Sudbury to Brantford. For part of the trip, he drove at 100 km/h. For the rest of the trip, he drove at 90 km/h. How far did he drive at each speed?

I have to put it in linear equations.

I think it is x+y= 470 and 100x+90y= 470

The answer is 200 at 100 km/h and 270 at 90 km/h.

But how do I get those numbers, by using substitution??

 

[BishopUser]

Hello caprija.

The proper equations are

100x + 90y = 470 where x is the number of hours driven at 100km/h and y is the number of hours driven at 90 km/h

x + y = 5 in the problem it says that the total time he took was 5 hours (this is the equation you messed up)

To solve by substitution you can solve for y in the 2nd equation
x + y = 5
y = 5 - x

so now we know that y = 5 - x , so in the first equation we can put that expression in place of y

100x + 90y = 470
100x + 90(5-x) = 470
100x + 450 - 90x = 470
10x = 20
x = 2

x = 2 which means that the number of hours he drove at 100 km/h is 2, which means the number of hours he drove at 90km/h is 3.

The problem asks for how many km he drove at each speed so simply take the hours and multiply them by the speed.

100km/h*2 hours = 200 km
90km/h*3 hours = 270 km

hope this helps!

 

[tacman]

Yes, you can use substitution to solve this problem. Let's break it down step by step:

1. First, we need to define our variables. Let x represent the distance Kareem drove at 100 km/h and y represent the distance he drove at 90 km/h.

2. Next, we can set up two equations using the information given in the problem. The first equation is x+y=470, representing the total distance of the trip. The second equation is 100x+90y=470, representing the total time it took Kareem to complete the trip.

3. Now, we can use substitution to solve for x or y in one of the equations. Let's choose the first equation, x+y=470, and solve for x. We can rearrange the equation to get x=470-y.

4. We can then substitute this value of x into the second equation, 100x+90y=470, to get 100(470-y)+90y=470. Simplifying this equation, we get 47000-100y+90y=470. Combining like terms, we get -10y=0, which means y=0.

5. Now, we can substitute this value of y into the first equation, x+y=470, to solve for x. Plugging in y=0, we get x+0=470, which means x=470.

6. Therefore, we know that Kareem drove 470 km at 100 km/h and 0 km at 90 km/h. This makes sense, as he drove at 100 km/h for the entire trip.

I hope this helps you understand how to use linear equations to solve word problems. Remember to define your variables, set up equations, and use substitution to solve for the unknown values. Good luck!