Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes f

Question

Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes first place, beating runner B by 10 m . Runner B takes second place, beating runner C by 12 m .

Problem 2.75 Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes first place, beating runner B by 10 m. Runner B takes second place, beating runner C by 12 m Part A By what time interval does runner A beat runner C? Express you answer as a fraction of the time that the runner A spent to finish the race. Express your answer using two significant digits tc Submit My Answers Give Up incorrect; Try Again; 2 attempts remaining Provide Feedback Continue

Explanation / Answer

here,

let the speed of of the runners be vA , vB and vC

for the same time interval

A beats B by 10 m

vA/vB = 100/90 = 10/9

and

B beats C by 12 m

vB/vC = 100/88 = 25/22

vA/vC = (vA/vB)(vB/vC) = (10/9)(25/22) = 250/198 = 100/79.2

so, when A travel 100 m then C travels 79.2 m

let the time taken by A be tA

tC - tA = ( 100 - 79.2)/vC

tC - tA = 20.8/vC

tC - tA = 20.8 /( vA * 79.2/100)

tC - tA = 20.8 * 100/ ( vA * 79.2)

tC - tA = tA * 0.26

so,

tC - tA = 0.26 * tA

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.