Question

${ \underline{ \boxed{ \frak{ \orange{question}}}}}$
A car travels 90 km in $\sf{ 2\dfrac{1}{2}hours}$.
a) How much time is required to cover 30 km with the same speed ?
b) Find the distance covered in 2 hours with the same speed.
_______________
Need full explanation!!
Don't Spam!!​

Answer 1

Given -

• Time given = $\sf{ 2\dfrac{1}{2}}$ and hours and 2 hours.

• Distance given = 90 km

To find -

• Time taken in part a and distance coveres in part b.

Solution -

In the question, we are provided with the distance and time in part a and time in part b. And we need to find the time taken in part a and distance covered in part b. For that, first in part a, we will convert the given time into minutes and then, we will solve the further question, and for part b, we will take the values from part a into part b, then we will solve the further question. Let's do it !

For Part A -

• Distance, d = 90km

• Time, t = $\sf{2\dfrac{1}{2}}$ = 150 minutes.

So -

Time taken to cover 90km is 150 mins therefore, it will take $\sf\frac{150}{90}$ mins to cover 1km.

Now -

We will equate the whole thing, we have obtained from above.

→ Time taken = Time taken in 1km × Total distance covered.

→ Time taken = 150/90 × 30

→ Time taken = 15/9 × 30

→ Time taken = 50 mins

$\therefore$ It will taken 50 mins to cover 30km.

For Part B -

• Distance covered = D

• Time taken = $\sf{2\dfrac{1}{2}}$ = 5/2 hours.

So -

5/2 hours are taken to cover 90km for part b, so the distance covered in 1km will be written as -

→ Distance coveres in 1km = 90 ÷ 5/2

→ Distance coveres in 1km = 2/5 × 90

→ Distance coveres in 1km = 36km

So -

Distance covered in 2 hours, will be written as -

→ Distance covered in 2 hours = 2 × 36km

→ Distance covered in 2 hours = 72 km

$\therefore$ In 2 hours, 72km distance will be covered.

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Answer 2

$\underline \mathfrak \red{Given-:}$

$\sf \bf \blue{given \: time = 2 \ \frac{1}{2} \: hours}$

$\sf \bf \blue{distance \: given = 90km}$

$\underline \mathfrak \red{to \:Find-:}$

→the time took in the 1st part and the distance cover in the second part !

$\sf \bf \pink{Answer-:}$

For part A)

$\sf \bf \purple{→2 \ \frac{1}{2} hours = (2 + \frac{1}{2} )}$

$\sf \bf \purple{→\frac{2 \times 2 + 1}{2} hours}$

$\sf \bf \purple{→ \frac{4 + 1}{2} \: hours}$

$\sf \bf \purple{ →\frac{5}{2} \: hours}$

$\sf \bf \purple{→ \frac{ 5}{2} \times 60 \: minutes \: (1 \: hour = 60 \: minutes)}$

$\sf \bf \purple{→5 \times 30}$

$\sf \bf \purple{→150 \: minutes}$

So , time require to cover 90km = 150 minutes !

Time required to cover 1km = 150/ 90 minutes !!

hence , time require to cover 30 km ,

$\sf \bf \purple{→ \frac{150}{90} \times 30 \: minutes}$

$\sf \bf \purple{→ \frac{15}{9} \times 30 \:minutes}$

$\sf \bf \purple{→ \frac{5}{3} \times 30 \: minutes}$

$\sf \bf \purple{→5\times 10 \: minutes}$

$\sf \bf \purple{→50 \: minutes}$

Therefore , it will take 50 minutes for car to cover 90 km !!!

For part B)

$\sf \bf \green{distance \: covered \: in2 \ \frac{1}{2}( = \frac{5}{2}) hours = 90 \: km}$

$\sf \bf \green{distance \: covered \: in \: 1 \: hour = \frac{90}{5}upon2 \: km}$

$\sf \bf \green{→90 \div \frac{5}{2} }$

$\sf \bf \green{→90 \times \frac{2}{5} }$

$\sf \bf \green{→ \frac{ 90 \times 2}{5} }$

$\sf \bf \green{→distance \: covered \: in \: 2 \: hours = ( \frac{90 \times 2}{5} ) \times 2km}$

$\sf \bf \green{→ \frac{90}{5} \times 2 \times 2 \: km}$

$\sf \bf \green{→18 \times 4 \: km}$

$\sf \bf \green{→ 74 \: km}$

hence , 72km of distance can be covered in 2 hours

(☘ Apologies for any mistakes in the above answer)