Question

what value of m will make 4x-7y=5 and 9x+my=3 parallel?

a car leaves town A at 10:00 a.m. and travels at a constant speed of 40 kph towards a town B. After 30 minutes, a bus leaves town A and travels towards town B at a constant speed of 56 kph. at what time will the bus catch up with the car and how far will they be from town A?

two towns A and B are 35 km apart. Carlo starts cycling from A towards B at 1:00 p.m. at 20 kph intil he is 16 kilometers away from A, when he changes his speed so that he arrives at B at 3:00 p.m. his friend Arnold leaves town B at 1:30 pm and cycles towards town A at a constant speed of 25 kph.find: a) carlo's speed in the last part of the journey. b) the time when Arnold reachestown A. c) the time when the two men meet.

Answer 1

Parallel lines have the same gradient.

The gradient of the first line is: 4/7

The gradient of the second line is: -9/m

Thus: 4/7 = -9/m

Solve for: m = ...

Answer 2

distance = speed multiplied by time.

Measure all distance in kilometres and all time in hours.

The car travels: c(t) = 40 t
The bus travels: b(t) = 56 (t - 0.5)

Solve for t when c(t)=b(t)

Answer 3

find: a) carlo's speed in the last part of the journey.

Carlos travels 16km at 20kph for: 20/16 hours.

Thus Carlos travels the remaining (35-16) km for (2-20/16)hours at:
(35-16)/(2-20/16)kph.

b) the time when Arnold reaches town A.

Arnold travels 35km at 25kph for: (35/25)hours.
Thus arriving at his destination at:
1:30+(35/25)

c) the time when the two men meet.
At 1:00+20/16 (when Carlos changes speed 16 km from A), Arnold has traveled:
((1+20/15)-1.5)25 kilometres.

Thus they have already passed.

At the time t they meet:
Arnold has traveled (t-1.5)25 kilometres
Carlos has yet to travel: (3-t)(35-16)/(2-20/16)

Solve: (t-1.5)25 = (3-t)(35-16)/(2-20/16)