# Word problems and liner equations

1. Sep 20, 2006

### caprija

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???????

2. Sep 20, 2006

### 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!