36. John and Priya went for a small picnic. After having their lunch Priya insisted to travel in a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. (i) Let speed of the current be z km/hr. then speed of the motorboat in upstream will be What is the relation between speed distance and time? (ii) (iii) Write the correct quadratic equation for the speed of the current ? OR (iv) What is the speed of current ?
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Step-by-step explanation:
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The relation between speed and time is speed×time = distance, quadratic equation of the situation is z²+30z-40 and the speed of current is 10 km/hr.
Given:
Speed of boat is 20 km/hr and boat goes 15 km and takes 1 hour more in upstream as compared with downstream.
To Find:
Relation between speed and time, quadratic equation and speed of current.
Solution:
Speed of current is z km/hr
At upstream speed = 20-z
At downstream speed = 20+z
Now, equation
[tex]\frac{15}{20-z}=\frac{15}{20+z} +1\\15*20+15z=15*20-15z+400-z^{2} \\z^{2}+30z-400\\[/tex]
This is the quadratic equation of the situation
[tex]z^{2}+30z-400\\ z^{2}+40z-10z-400=0\\ z(z+40)-10(z-40)=0\\(z+40)(z-10)=0\\z=-40, z=10[/tex]
Ignoring the negative value the speed of current is 10 km/hr
Hence, the relation between speed and time is speed×time = distance, quadratic equation of the situation is z²+30z-40 and the speed of current is 10 km/hr.
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