Question

an aeroplane takes one hour and forty minutes to covers a distance of 1350 km. whereas a helicopter takes two hours and forty minutes to cover 600km. find the ratio of the speed of the two.

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Answer 1

GIVEN:

• Time taken by the aeroplane to cover the distance = 1 hr 40 min.
• Distance covered by the aeroplane = 1350 km.
• Time taken by the helicopter to cover the distance = 2 hr 40 min.
• Distance covered by the aeroplane = 600 km

TO FIND:

• What is the ratio of the speed of the aeroplane and helicopter ?

SOLUTION:

We have to find the speed of an aeroplane

Let the speed of the aeroplane be 's' km/hr

• Time taken = 1 hr 40 min
• Distance covered = 1350 km

$\bf{\star \: Time = 1 \: hr \: 40 \: min}$

$\bf{\star \: Time = 1 + \dfrac{40}{60} \: hr}$

$\bf{\star \: Time = \dfrac{60+40}{60} \: hr}$

$\bf{\star \: Time = \cancel\dfrac{100}{60} \: hr}$

$\bf{\star \: Time = \dfrac{5}{3} \: hr}$

We know that the formula for finding the speed of the aeroplane is:-

$\large{\boxed{\bf{\star \: Speed = \dfrac{Distance \: covered}{Time \: Taken} \: \star}}}$

According to question:-

On putting the given values in the formula, we get

$\rm{\hookrightarrow s = \dfrac{\cancel{1350} \times 3}{\cancel{5}} \: km/hr }$

$\bf{\hookrightarrow s = 810 \: km/hr }$

• Speed of aeroplane = 810 km/hr

Now, we have to find the speed of helicopter

Let the speed of the helicopter be 's'' km/hr

• Time taken = 2 hr 40 min
• hr 40 minDistance covered = 600 km

$\bf{\star \: Time = 2 \: hr \: 40 \: min}$

$\bf{\star \: Time = 2 + \dfrac{40}{60} \: hr}$

$\bf{\star \: Time = \dfrac{120+40}{60} \: hr}$

$\bf{\star \: Time = \cancel\dfrac{160}{60} \: hr}$

$\bf{\star \: Time = \dfrac{8}{3}\: hr}$

According to question:-

On putting the given values in the formula, we get

$\rm{\hookrightarrow s' = \dfrac{\cancel{600} \times 3}{\cancel{8}} \: km/hr }$

$\bf{\hookrightarrow s' = 225 \: km/hr }$

• Speed of helicopter = 225 km/hr

❮ Ratio of aeroplane and helicopter = Speed of aeroplane/speed of helicopter ❯

According to given conditions:-

$\bf{\longrightarrow Ratio = s : s'}$

$\bf{\longrightarrow Ratio = 810: 225}$

$\large{\boxed{\bf{\star \: Ratio = 18:5 \: \star}}}$

______________________

Answer 2

Step-by-step explanation:

Time taken by the aeroplane to cover the distance = 1 hr 40 min.

Distance covered by the aeroplane = 1350 km.

Time taken by the helicopter to cover the distance = 2 hr 40 min.

Distance covered by the aeroplane = 600 km

TO FIND:

What is the ratio of the speed of the aeroplane and helicopter ?

SOLUTION:

We have to find the speed of an aeroplane

Let the speed of the aeroplane be 's' km/hr

Time taken = 1 hr 40 min

Distance covered = 1350 km

\bf{\star \: Time = 1 \: hr \: 40 \: min}⋆Time=1hr40min

\bf{\star \: Time = 1 + \dfrac{40}{60} \: hr}⋆Time=1+

60

40

hr

\bf{\star \: Time = \dfrac{60+40}{60} \: hr}⋆Time=

60

60+40

hr

\bf{\star \: Time = \cancel\dfrac{100}{60} \: hr}⋆Time=

60

100

hr

\bf{\star \: Time = \dfrac{5}{3} \: hr}⋆Time=

3

5

hr

We know that the formula for finding the speed of the aeroplane is:-

\large{\boxed{\bf{\star \: Speed = \dfrac{Distance \: covered}{Time \: Taken} \: \star}}}

⋆Speed=

TimeTaken

Distancecovered

⋆

According to question:-

On putting the given values in the formula, we get

\rm{\hookrightarrow s = \cancel\dfrac{1350 \times 3}{5} \: km/hr }↪s=

5

1350×3

km/hr

\bf{\hookrightarrow s = 810 \: km/hr }↪s=810km/hr

Speed of aeroplane = 810 km/hr

Now, we have to find the speed of helicopter

Let the speed of the helicopter be 's'' km/hr

Time taken = 2 hr 40 min

hr 40 minDistance covered = 600 km

\bf{\star \: Time = 2 \: hr \: 40 \: min}⋆Time=2hr40min

\bf{\star \: Time = 2 + \dfrac{40}{60} \: hr}⋆Time=2+

60

40

hr

\bf{\star \: Time = \dfrac{120+40}{60} \: hr}⋆Time=

60

120+40

hr

\bf{\star \: Time = \cancel\dfrac{160}{60} \: hr}⋆Time=

60

160

hr

\bf{\star \: Time = \dfrac{8}{3}\: hr}⋆Time=

3

8

hr

According to question:-

On putting the given values in the formula, we get

\rm{\hookrightarrow s' = \cancel\dfrac{600 \times 3}{8} \: km/hr }↪s

′

=

8

600×3

km/hr

\bf{\hookrightarrow s' = 225 \: km/hr }↪s

′

=225km/hr

Speed of helicopter = 225 km/hr

❮ Ratio of aeroplane and helicopter = Speed of aeroplane/speed of helicopter ❯

According to given conditions:-

\bf{\longrightarrow Ratio = s : s'}⟶Ratio=s:s

′

\bf{\longrightarrow Ratio = 810: 225}⟶Ratio=810:225

\large{\boxed{\bf{\longrightarrow Ratio = 18:5}}}

⟶Ratio=18:5

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