Linear Worded Problem

• Jan 17th 2010, 01:47 AM
user_5
Linear Worded Problem
A car journey of 300 km lasts 4 h. Part of this journey is on a freeway at an average speed of 90 km/h. The rest is on country roads at an average speed of 70 km/h.

Let T be the time (in hours) spent on the freeway.

a) In terms of T, state the number of hours travelling on country roads.
$4-T$

b) State:
i. The distance travelled on the freeway in terms of T
Distance Travelled= $90T$

ii. The distance travelled on country roads in terms of T.
Distance Travelled = $70(40-T)$

c Find:
i. T
I'm having trouble finding T, Can someone help?

ii The distance travelled on each type of road.
• Jan 17th 2010, 01:56 AM
earboth
Quote:

Originally Posted by user_5
A car journey of 300 km lasts 4 h. Part of this journey is on a freeway at an average speed of 90 km/h. The rest is on country roads at an average speed of 70 km/h.

Let T be the time (in hours) spent on the freeway.

a) In terms of T, state the number of hours travelling on country roads.
$4-T$

b) State:
i. The distance travelled on the freeway in terms of T
Distance Travelled= $90T$

ii. The distance travelled on country roads in terms of T.
Distance Travelled = $70(\bold{\color{red}4}-T)$ <<<<<< typo

c Find:
i. T
I'm having trouble finding T, Can someone help?

ii The distance travelled on each type of road.

All your considerations are OK.

Put the 2 equations together:

$90T + 70(4-T) = 300$

Solve for T.
Spoiler:
I've got T = 1
• Jan 17th 2010, 02:01 AM
user_5
Thanks! and yeah, that was a typo! my bad.