The speed of a bike increases by 3 km/hr after every 1 hour. If the distance travelled by the bike in 1st hour is 22 km, the find the total distance travelled by the bike in 12 hours.

Solution

Since, the speed of the bike increases by 3 km/hr after every 1 hour, therefore the bike will travel 3 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 22 km Distance travelled by the bike in 2nd hour = 22 + 3 = 25 km Distance travelled by the bike in 3rd hour = 25 + 3 = 28 km This form an AP i.e. 22, 25, 28………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 = 22 and d = common difference = 3 Therefore, distance travelled in 12 hours = (12/2){2 × 22 + (12 – 1) × 3} = (12/2)(44 + 33) = 462 km