QUADRATIC EQUATIONS
A man riding on a bicycle covers a distance of 60 km in a direction of wind and comes back to his original position in 8 hours. If the speed of the wind is 10 km/hr. Find the speed of the bicycle.
Sol.
SPEED
Let the speed of bicycle be x km/hr
| | |
| | |
| | |
| | |
SPEED
DISTANCE
TIME
= DISTANCE
SPEED
In the direction
of wind
Against the direction
of wind
60 km
(x + 10) km/hr
60
60 km
(x – 10) km/hr
60
x km/hr
10 km/hr
x km/hr
What we have to find in this sum ?
x + 10
x – 10
60 km
Speed in the direction of wind = (x + 10) km/hr
Speed against the direction of wind = (x – 10) km/hr
Total time taken = 8 hours
+
= 8
As per the given condition
homework
+
= 8
∴
= 8
∴
=
∴
=
Dividing throughout by 2 we get,
=
=
∴
=
∴
=
∴
=
∴
=
∴
=
=
∴
∴
∴
∴ The speed of the bicycle is 20 km/hr
1
‘-’ sign means subtracting
Find two factors of 100 in such a way that by subtracting factors we get middle number.
100 × 1 = 100
Since last sign is ‘-’ Give middle sign to the bigger factor & opposite sign to smaller factor.
20
5
100
-
+
60
2
15
A man riding on a bicycle cover a distance of 60 km in a direction of wind and comes back to his original position in 8 hours. If the speed of the wind is 10 km/hr. Find the speed of the bicycle.
Sol.
Let the speed of bicycle be x km/hr
As per the given condition