Question

With a uniform speed, a car covers the distance in 8 h. Had the speed been increased by 4 km/h, the same distance could have been covered in
$7 \times \frac{1}{2} hr$
What is the distance covered?
(1) 640 km
(2) 480 km
(3) 420 km ​

Answer 1

Answer:

(2) 480 km

Step-by-step explanation:

[Before I begin, I would like to state a small mistake in the question. The second time given should be 7 + 1/2 hrs and not 7 × 1/2 hrs. Only then we'll get the answer in the option]

We know,

$speed(v) \: = \frac{distance(d)}{time(t)} \\ d = v \times t$

Since the distance traveled in both the cars is the same, the product of speed and time in both cases will be the same.

Case 1

Speed = v km/h

Time = 8 hrs

So,

$d = v \times 8 = 8v$

Case 2

Speed = (v + 4) km/h

Time = (7 + 1/2) hrs = 15/2 hrs

$d = (v + 4) \times \frac{15}{2} \\ = \frac{15v + 60}{2}$

So, equating the products,

$8v = \frac{15v + 60}{2} \\ = > 16v = 15v + 60 \\ = > 16v - 15v = 60 \\ = > v = 60$

Putting v = 60 in Case 1, we get,

$d = 8v = 8 \times 60 = 480$

So, the distance covered = 480 km/h

Hope this helps

Have a nice day