A magician can reach his auditorium in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed
Answers
Answer:
A magician can reach his auditorium in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.
The magicians speed is 5 km/hr
Explanation:
Speed = distance / time
Let us assume that the distance to the auditorium is x km
Time taken = 30 hours
Speed = x km / 30 hrs
= x/30 km/hr
Find the reduction of speed by 1/15th
1 - 1/15 = 14/15
Find the reduced speed = 14/15 × x/30km/hr
= 14x/450 km/hr
We are now told that using this speed he covers 10km less in the time
Therefore speed = 14x/450 km/hr
time taken = 30 hours
distance travelled = (x - 10) km
We know that speed = distance / time
14x / 450 = (x-10) / 30
⇒ x - 10 = (14x × 30) / 450
⇒ x - 10 = 14x/15
⇒ 14x = 15x - 150
⇒ 15x - 14x = 150
x = 150
Therefore the distance to the auditorium is 150 km
Speed = distance / time
= 150 km / 30 hours
= 5 km/hr
Therefore the speed of the magician is 5 km/hr