Answer:
Step-by-step 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
[tex]<=> 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[/tex]
(d)
[tex]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[/tex]
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
