Question

A car starts running with the initial speed of 40 kmph, with its speed increasing every hour by 5 kmph. How many hours will it take to cover a distance of 385 km?

• A. 9 hrs
• B. $9\frac{1}{2}$ hrs
• C. $8\frac{1}{2}$hrs
• D. 7 hrs

Answer 1

Answer: (D)

7 hrs

Answer 2

There is an Arithmetic Progression here,
$40 + (40+5)+ (40+5+5) .....n \;terms = 385$
So, sum of terms = 385
first term = 40 and common difference = 5
\Rightarrow\;$$S = \frac{n}{2}[2a + (n-1)\times d]
\Rightarrow\;$$385 = \frac{n}{2}[80+5n-5)
\Rightarrow\;$$770 = n[75+5n]
\Rightarrow\;$$154 = n(15+n)
\Rightarrow\;$$n = 7
So it takes 7 hours to cover a distance of 385 kms.

The correct option is (D): 7 hrs