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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    distance = rate * time a) PQ = 2*x+(3/2)(x-3)

  2. anonymous
    • 5 years ago
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    b) PQ=3*(x+1)

  3. anonymous
    • 5 years ago
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    c) we know the distance there = the distance back, so (2x+(3/2)(x-3)=(x+1)

  4. anonymous
    • 5 years ago
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    so x=11/5 from c, so the distance is 3*(11/5+1) PQ=3*(15/6)=15/2

  5. anonymous
    • 5 years ago
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    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

  6. anonymous
    • 5 years ago
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    really sorry to interrupt you but for c),my answer booklet says it's 48km/h.

  7. anonymous
    • 5 years ago
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    Your c here asks for a distance, not a rate, so something is wrong somewhere : )

  8. anonymous
    • 5 years ago
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    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.

  9. anonymous
    • 5 years ago
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    ooh, I made a silly error!

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

  11. anonymous
    • 5 years ago
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    x=3! Not 11/5. The explanation is right : )

  12. anonymous
    • 5 years ago
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    Your explanation?

  13. anonymous
    • 5 years ago
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    yeah, I just forgot a factor of 3 when I did my algebra to solve for x, so the numbers are off

  14. anonymous
    • 5 years ago
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    yeah but anyways,you bothered to help me :D so kind of you..Thanks again.

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