Question

3. The distance between two houses, P and Q, is 200 km.
Joe travelled by car from P to Q at an average speed of x km/h.
(a) Write down an expression, in terms of x, for the number of hours he took to travel
from P to Q.
(b) He returned from Q to P at an average speed of (x + 5) km/h.
Write down an expression, in terms of x, for the number of hours he took to travel
from Q to P.
[1]
(c) The total time he took to go from P to Q and to return from Q to P was 8 hours.
(i) Write down an equation in x and show that it simplifies to
x2 - 45x – 125 = 0.
[4]
(ii) Solve the equation x2 – 45x – 125 = 0, giving each answer correct to 2 decimal
places.
[4]
(iii) Calculate, correct to the nearest minute, the time he took to travel from P to Q.
[2]

Answer 1

Answer:

Step-by-step explanation:

A)The number of hours he took to travel from P to Q.

=200/x

b) 200/(x+5)

c) 200/x+200/(x+5) =8

200( 1/x+1/x+5)=8

(x+5+x)/x(x+5)=8/200=1/25

25(2x+5)=x²+5x

x²-45x-125=0

********************

(ii) x²-45x-125=0

x={ 45±√(45²-4*125)}/2

={ 45±√(2025-500)}/2

={ 45±√(2025-500)}/2

={45±39)/2= 45+39/2=84/2=42 km/hr

4.(iii)200/42=4.76 hrs

Answer 2

Answer:

p=1

q=2

Step-by-step explanation: