Question

The distance between two cities A and B is 400km. A car leaves from A towards B at a speed of 90kmph, at the same time another car leaves from B towards A at 110kmph.

-
a) Write the equations that give the distance as function of time.
b) Represent them graphically. V
c) Find the distance they have traveled to meet each other and the time invested.

Answer 1

a. Distance = 400 - 200t

b. see attached graph

c. A travelled 180 km, B travelled 220 km, both took 2 hours.

Explanation:

Given

distance = 400

A = 90 km/h

B = 110 km/h

A & B drive towards each other

Solutions

a) equation

Let

t = elapsed time in hours,

D(t) = distance between two drivers

D(t) = 400 - (A+B) t

D(t) = 400 - 200t ......................(1)

b. graph : for graph, see attached figure.

c. Distance and time

Time:

solve for t with the distance D(t) = 0 using equation (1)

0 = 400 - 200 t

200t = 400

t = 2 hours

distance travelled by A = 2 hours * 90 km/h = 180 km

distance travelled by B = 2 hours * 110 km/h = 220 km