Question

Anyone willing to help? Question 2 only

Answer 1

Explanation:

Hello,

(a) Peter cycle at an average speed of x km/h

it means that he is doing x km in 1 hour

so to do 40 km he needs 40/x hour

(b) it means that he was doing x-5 km/h

so it took 40/(x-5) hour

(c) 1 hour 20 minutes correspond to 1+20/60=1+1/3=4/3 hour as 1 hour is 60 minutes

so we can write

40/(x-5)=40/x+4/3

`<=> 3*40x=3*40(x-5)+4x(x-5) \ \ \ \text{multiply by 3x(x-5) both sides}\\<=> 120x =120x-600+4x^2-20x\\<=>4x^2-20x-600 = 0\ \ \ \text{divide by 4} \\<=> x^2-5x-150=0`

(d)

`x^2-5x-150=0\\<=> x^2+10x-15x-150=0\\<=> x(x+10)-15(x+10)=0\\<=> (x-15)(x+10)=0\\\\<=> x = 15 \ \ or \ \ x=-10`

the speed is positive so we take the positive solution which is 15

the speed is 15 km/h

hope this helps

do not hesitate if you need more information