How far did she drive at 70km/h?

Question

Maria drove from Owen Sound to Ottawa, a distance of 550km. The trip took 7h. Maria drove at 70km/h for part of the trip, and 85km/h for the remainder of the trip. How far did she drive at 70km/h?

Answer 1

Let say :

 

x is the number of hours Maria drove at 70km/h

y is the number of hours Maria drove at 85km/h.

 

We know that   x + y = 7

 

 

The distance is determined by the following equation d = ts where d is the distance, t is the time, and s is the speed.

So we can determine the distance Maria drove at 70km/h which is 70x, and the distance she drove at 85km/h which is 85y.

Thus we have the total distance 70x + 85y = 550

 

 

We thus have

x + y = 7

70x + 85y = 550

 

Then we will replace x by 7 - y in the second equation and solve:

 

70x + 85y = 550

70(7 - y) + 85y = 550

490 - 70y + 85y = 550

-70y + 85y = 550 - 490

15y = 60

y = 60 / 15

y = 4

 

 

Then we can replace y by 4 in the first equation to find x:

 

x + y = 7

x + 4 = 7

x = 7 - 4

x = 3

 

Maria drove 3 hours at 70km/h, which is 210 kms (3x70) and 4 hours at 85km/h, which is 340kms (4x85).

 

 

 

Answer 2

 

 

Hi Loppy

Here are the steps to be followed

Let X = distance coverd with 70km/hr

Y =550 - X = distance covered with 85 km/hr

Let t1 and t2 be the rspective time taken

then t1 +t2 = 7 hrs

As speed = distance / time

t1 = X/ 70 and t2 = Y/85 =(550-X )/85

 

X/70 + (550- X)/ 85 = 7

 15 X= 7*70*85 - 70*550 = 3150

X = 210 km anf 550 - X = Y =340 km

The distance covered with 70 km/hr is 210 km