Question

A car covers half the distance at a speed of 21 km/h and remaining half at a speed of 24 km/h. the time taken for the journey is 10 hours. find total distance? ??​

Answer 1

Answer:

• Total distance covered by car = 224 km.

Step-by-step explanation:

Given:

• Car covers half the distance at a speed of 21 km/h.
• And remaining half at a speed of 24 km/h.
• Time taken for journey = 10 hours.

To Find:

• Total distance travelled by car.

Formula used:

• Distance = speed × time

Now,

• Let total distance = d km
• Time taken to travel 1st half = x hr
• Time taken to travel 2nd half = (10 - x) hr

Now, we know that

⇒ Distance = Speed × Time

∴ Case 1). For 1st half:

$\implies{\sf{Distance = Speed \times Time}}$

$\implies{\sf{\dfrac{d}{2} = 21 \times (x)}}$

$\implies{\sf{\dfrac{d}{2} = 21 x}}$

$\implies{\sf{d = 42x\;\;\;\;..(1)}}$

∴ Case 2). For 2nd half:

$\implies{\sf{Distance = Speed \times Time}}$

$\implies{\sf{\dfrac{d}{2} = 24 \times (10-x)}}$

$\implies{\sf{d =48(10-x)\;\;\;\;\;..(2)}}$

Now, Distance covered in 1st half = Distance covered in 2nd half

⇒ 42x = 48(10 - x)

⇒ 42x = 480 - 48x

⇒ 42x + 48x = 480

⇒ 90x = 480

⇒ x = 480/90

⇒ x = 5.33

Now, to find total distance put the value of x in equation (1).

⇒ d = 42x

⇒ d = 42 × 5.33

⇒ d = 224 km

Hence, Total distance covered by car = 224 km.

Answer 2

Given :-

• A car covers half the distance at a speed of 21 km/h
• Remaining half at a speed of 24 km/h.
• Time taken for the journey is 10 Hours

To find :-

• Total distance traveled by car = ?

We know that :-

• Distance = Speed × Time.

Now,

• Let Total Distance = d km.
• Time taken to travel 1st half = h hour.
• Time taken to travel 2nd half = (10 - h) hours.

By putting formula in both cases we get :-

1) Case 1st :-

→ Distance = Speed × Time

→ d/2 = 21 * (h)

→ d/2 = 21h

→ d = 42h . . . . . (1)

2) Case 2nd :-

→ d/2 = 24 * (10 - h)

→ d = 48(10 - h) . . . . . (2)

So now,

• Distance covered in 1st half = Distance covered in 2nd half.

→ 42h = 48(10 - h)

→ 42h = 480 - 48h

→ 42h + 48h = 480

→ 90h = 480

→ h = 5.33.

Now, If we have to find Total Distance so we need to put the value of h into equation 1st.

d = 42h

→ d = 42 * 5.33

→ d = 224km.

So, Total Distance covered by car is = 224km.