Question

1. A tortoise is running on a long, moving sidewalk. Her pedometer doesn't report her speed, but she knows that—since she got on—she's been running for 40 minutes and that she's traveled 3 kilometers. Unfortunately, she realizes she left her suitcase on the ground just before she got on the sidewalk. Since she's too short to climb over the handrails, she decides to turn around and run at the same speed back to her suitcase. If it takes her 2 hours to return to her suitcase, how fast (in kilometers per hour) was the moving sidewalk moving? How fast (in kilometers per hour) was the tortoise running?

Answer 1

Answer:

the sidewalk speed q = 3km/hr

the tortoise speed p is 1.5 km/hr

Step-by-step explanation:

From the given information:

let the speed of the tortoise be p  & the speed of the sidewalk be q

she's been running for 40 minutes (40/60 = 2/3) and that she's travelled 3 kilometres

Thus,

p + q = $\dfrac{3}{\dfrac{2}{3}}$

p + q = 9/2

p + q = 4.5 ----- (1)

when returning, she travelled 3km in 2 hours

i.e. -p + q = 3/2

-p + q = 1.5   ----- (2)

Thus, by using the elimination method for equation (1) and (2)

  p + q = 4.5  ----- (1)

-p + q   = 1.5 ----- (2)  

      2q =  6              

q = 6/2

q = 3 km/hr

From equation (1)

p + q = 4.5

p + 3 = 4.5

p = 4.5 - 3

p = 1.5 km/hr

Therefore, the sidewalk speed q = 3km/hr and the tortoise speed p is 1.5 km/hr