RV-13-001 · Bounds on journey speed and a decision
A journey is recorded as 150 km, correct to the nearest km, and 137 minutes, correct to the nearest minute.
(a) Calculate the lower and upper bounds for the average speed in km/h. Give each bound to 2 decimal places.
(b) Can you be certain that the average speed exceeded 50 km/h? Explain.
Part (a)
Bounds on Average Speed ("DuSTy" & Bounds Table)
Booklet p. 54, p. 64 & p. 65
Method
1) Find LB and UB of distance and time
2) Speed_LB = (D_LB ÷ T_UB) × 60; Speed_UB = (D_UB ÷ T_LB) × 60
3) Compare Speed_LB with speed limit
Worked Example (RV-13-001 · Part (a))
Calculate the lower and upper bounds for the average speed in km/h. Give each bound to 2 decimal places.
From Bounds Table (p. 65): For Division, and
1) Distance bounds 149.5, 150.5; time bounds 136.5, 137.5 minutes.
2) For the lower speed use lower distance and upper time; multiply by 60.
3) 65.24 km/h
4) For the upper speed use upper distance and lower time; multiply by 60.
5) 66.15 km/h
Lower 65.24 km/h; upper 66.15 km/h.
Part (b)
Bounds on Average Speed ("DuSTy" & Bounds Table)
Booklet p. 54, p. 64 & p. 65
Method
1) Find LB and UB of distance and time
2) Speed_LB = (D_LB ÷ T_UB) × 60; Speed_UB = (D_UB ÷ T_LB) × 60
3) Compare Speed_LB with speed limit
Worked Example (RV-13-001 · Part (b))
Can you be certain that the average speed exceeded 50 km/h? Explain.
From Bounds Table (p. 65): For Division, and
1) The lower speed bound is 65.236364… km/h; it exceeds the threshold.
Yes.