Question

A cyclist rode From P to Q for 2 hours at an average speed of x km/h and then for 3/2 hours at (x-3)km/h

a) Find in terms of x an expression for the distance of PQ.
After he had rested for half an hour at Q,he rode back from Q to P for 3 hours at the speed of (x+1) km/h
b)Find in terms of x,an expression of the distance PQ
c)Form an equation in x and find the distance of PQ
d)Find the average speed for the two way journey

Answer 1

distance = rate * time

a) PQ = 2*x+(3/2)(x-3)

Answer 2

b) PQ=3*(x+1)

Answer 3

c) we know the distance there = the distance back, so (2x+(3/2)(x-3)=(x+1)

Answer 4

so x=11/5 from c, so the distance is 3*(11/5+1)
PQ=3*(15/6)=15/2

Answer 5

so using the total distance of 2*(15/2)=15km
and the total time of 2+(3/2)+3hours

we get 15km per 13/2 hours. Multiplying top and bottom by 2/13, we get

15*(2/13)=30/13 km/h

Answer 6

really sorry to interrupt you but for c),my answer booklet says it's 48km/h.

Answer 7

Your c here asks for a distance, not a rate, so something is wrong somewhere : )

Answer 8

I used (2x+(3/2)(x-3)=3(x+1) instead of (2x+(3/2)(x-3)=(x+1) and i got x=15..Then i substituted x=15 into 3(x+1) and got 48 km/h.
Anyways, many thanks for your help :D really helped me to solve this qn.

Answer 9

ooh, I made a silly error!

Answer 10

Nah..if not for your explanation about distance here = distance there,it would have taken me longer to solve this qn :D

Answer 11

x=3! Not 11/5. The explanation is right : )

Answer 12

Your explanation?

Answer 13

yeah, I just forgot a factor of 3 when I did my algebra to solve for x, so the numbers are off

Answer 14

yeah but anyways,you bothered to help me :D so kind of you..Thanks again.