Question

A cyclist plans to cover the distance of 240km . He calculated that if he is going to ride 8.4km/h faster than planned, he will cover the same distance 105minutes earlier. At what speed did he originally plan to ride?

Answer 1

Answer:

Radius of the wheel =r=

2

60

=30 cm

Circumference of the wheel =2πr=2×

7

22

×30=

7

1320

cm

Distance covered in 1 revolution =

7

1320

cm

Distance covered in 140 revolutions =

7

1320

×140=26400 cm=264 m=

1000

264

km

Distance covered in one minute = Distance covered in 140 revolutions =

1000

264

km

Step-by-step explanation:

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Answer 2

Answer:

30km/h

Step-by-step explanation:

105minutes = 1,75 hour = 7/4

t - t₁ = $\frac{s}{v} - \frac{s}{v+8,4} =\frac{7}{4}$

=> $\frac{240}{v} - \frac{240}{v+8,4} = \frac{7}{4}$

=> 240 $(\frac{1}{v} - \frac{1}{v+8,4}) = \frac{7}{4}$

=> $(\frac{1}{v} - \frac{1}{v+8,4}) = \frac{7}{960}$

=> $7v^{2} + 58.8 v - 8064 = 0$

• $ax^{2} +bx+c=0 (a\neq 0)$

• Δ=$b^{2} - 4ac$

• x₁,₂ = (-b±√Δ) / 2a

Δ = $(58.8)^{2} - 4. 7 . (-8064) = 229249.44$

v₁ = $\frac{-58.8 + \sqrt{229249.44} }{2.7} = 30 km/h$ ------- (oki)

v₂ = $\frac{-58.8 - \sqrt{229249.44} }{2.7} = -38.4 km/h$ ------ (no)

=> v = 30 km/h