Question

Mr. Smith's art class took a bus trip to an art museum. The bus averaged 65 miles per hour on the highway and 25 miles per hour in a city. The art museum is 375 miles away from the school, and it took the class 7 hours to get there. Use Cramer's Rule to find how many hours the bus was on the highway and how many hours it was driving in the city.

Answer 1

since no ones answering heres my answer..XD



Let x be the number of miles traveled via highway
Let y be the number of mile traveled via city routes

Then:

(1) x+y = 375
(2) x/65 + y/25 = 7 <==> (1/65)x + (1/25)y = 7

So our matrix looks like this:

[ 1 1 ] [x] = [375]
[ 1/65 1/25 ] [y] [ 7 ]

(Below the |'s are determinants, as per Cramer's Rule)
x =
| 375 1 |
| 7 1/25 |
-------------------
| 1 1 |
| 1/65 1/25 |

= [(375*1/25)-(1*7)] / [1*1/25 - 1*1/65]
= 8/ (8/325)
= 325 miles

y =
| 1 375 |
| 1/65 7 |
-------------------
| 1 1 |
| 1/65 1/25 |

= [1*7 - (375*1/65)] / [1*1/25 - 1*1/65]
= (16/13) / (8/325)
= 50 miles

So x = 325 miles. With average speed 65mi/h:

325mi/65mi/h = 5 hours

y = 50 mi. At average speed 25mi/h:

50mi/25mi/h = 2 hours

So, we travel 5 hours on the highway, and 2 hours on city streets.