Wednesday, 22 April 2015

Challenger: Linear Inequalities


Adapted from wiley.com

Two speed boats are racing along a section of a lake.
The speed limit along this section of the lake is 50 km/h. Ray is travelling 6 km/h faster than Stephen and the sum of the speeds at which they are travelling is at a speed greater than 100 km/h.

a. Write an inequality and solve it to describe all possible speeds that Stephen could be travelling at.
b. Verify if Stephen's lowest possible speed was over the speed limit.
c. The coast guard issued a warning to Ray for exceeding the speed limit on the lake. Explain why the police were justified in issuing a warning to Ray. 

10 comments:

  1. Ray = (100+6)/2
    = 53
    Stephen = 47
    Stephen's lowest speed is not over the limit
    Ray was travelling at the speed of 53km/h and is over the speed limit. And therefore, was issued a warning

    ReplyDelete
  2. a)Let Stephen's speed be x
    0100
    If x is 50, Ray's speed would be 56, exceeding the speed limit

    ReplyDelete
    Replies
    1. a)x≤50
      b) Stephen's lowest speed is 1km/h which is under the speed limit
      c) Let Ray's speed be x+6
      ((x+6)+x)>100
      If x is 50, Ray's speed would be 56, exceeding the speed limit

      Delete
  3. Let stephen's speed b x
    a)x≤44
    b)no.His lowest speed is 47.5km/h
    c)Ray was travelling in a minimum speed of 53.5km/h, which exceeds the speed limit,:.he was issued a warning.

    ReplyDelete
  4. a)x≤44
    b)As it is either 44 or under 44 , he cannot be above the 50km/h speed limit.
    c)Minimum speed=100-44
    =56km/h
    He exceeded the speed limit , thus the coast guard issued him a warning.

    ReplyDelete
  5. a) x>100-6/2 = 94/2 = 47
    b) x = Stephen's Speed
    Lowest possibility of x would be 48, so it is not over the speed limit
    c)If Stephen lowest possible speed is 48km/h, then Ray's speed should be 54km/h, which is over the speed limit.

    ReplyDelete
  6. a)47≤x≤50
    b)no.100-6=94
    94/2=47
    47<50
    c)ray was travelling at a speed of 47+6=53(which os over the speed limit)
    53>50 so the police were justified in issuing a warning to Ray.

    ReplyDelete
  7. a) 47≤x≤50
    b) No, 100-6=94, 94/2=47
    c) Ray was driving above the speed limit, so the police were justified in issuing a warning to Ray

    ReplyDelete
  8. a) Stephen's possible speeds = > 47

    b) Lowest = > 47
    Therefore, Stephen's speed is not over the speed limit.

    c) Ray's speed = Stephen's speed + 6km/h
    Stephen's lowest possible speed > 47
    Ray's lowest speed = > 47 + 6
    = 53 (exceeds speed limit)

    Therefore, as Ray had exceeded the speed limit, the coast guard is right to issue him a warning.

    ReplyDelete
  9. a)stephens possible speed 47≤x≤50
    b)47>50 therefore it was not over the speed limit
    c) rays speed exceeded 50 so the police had the rights to issue him a warning

    ReplyDelete