The speed of a bike increases by 4 km/hr after every 1 hour. If the distance travelled by the bike in 1 st hour is 30 km, the find the total distance travelled by the bike in 12 hours.

Solution

Since, the speed of the bike increases by 4 km/hr after every 1 hour, therefore the bike will travel 4 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 30 km Distance travelled by the bike in 2nd hour = 30 + 4 = 34 km Distance travelled by the bike in 3rd hour = 34 + 4 = 38 km This form an AP i.e. 30, 34, 38………distance travelled in 12th hour Therefore, total distance travelled by the bike in 12 hours = sum of the AP Distance travelled in 12 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 12, a = 1st term = 30 and d = common difference = 4 Therefore, distance travelled in 12 hours = (12/2){2 × 30 + (12 – 1) × 4} = (12/2)(60 + 44) = 624 km