a mathematican travelled 300km to attend a confirence during his talk he said had my average speedmincreased by 10 km per hrs i could have reached here one hour earlier what was the average speed
Answers
Answer:
1. Let the average speed be 'x' km/h
2. Distance travelled = 300 km.
3. So time taken 't' = Distance⁄speed = 300⁄x hours
4. This time would be reduced by 1 h. So the new time = (300⁄x-1) hours
5. For that, the average speed must increase by 10 km/h. So the new speed = (x+10)
6. The distance remains the same. We have: Distance = time × speed = (300⁄x-1) × (x+10)
⇒ Distance = 300 = (300⁄x-1) × (x+10) ⇒ 300 = [(300-x)⁄x]×(x+10)
⇒ 300x = (300-x)(x+10) ⇒ 300x = 300x - x2 +3000 -10x
⇒ 0 = -x2+3000 -10x ⇒ x2+10x = 3000
7. The coefficient of x is 10.
• Half of the coefficient is 10⁄2 = 5
• Square of this is 52 = 25
8. Add this square to both sides. We get:
x2+10x+25 = 3000+25 ⇒ x2+10x+25 = 3025
9. But x2+10x+25 is (x+5)2. So we can write:
10. (x+5)2 = 3025 ⇒ (x+5) = √3025 = 55 ⇒ x = 50
• So the average speed is 50 km/h
Check: Put x = 50 in (6). We get: 502 + (10 × 50) = 2500 + 500 = 3000
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
Given.
Distance = 100km
If average speed been increased by 10 kilometres per hour, I could have reached here one hour earlier
Formula used.
Average speed =
Let the sum of time taken be x
Average speed = sum of distance /sum of time
New average speed = average speed + 10
+ 10