Answer:
3.46 mph
Step-by-step explanation:
Speed of Tara bicycling without wind effect = 15mph
let the speed of wind be x mph
If she cycles against the wind then her speed will be decrease by the amount as the speed of wind
Then,
Speed of Tara bicycling against wind effect = (15-x)mph
distance traveled by Tara against wind = 10 miles
we know that
time = distance by speed
time taken by Tara while traveling against wind = 10/(15-x)
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If she cycles with the wind then her speed will be increase by the amount as the speed of wind
Then,
Speed of Tara bicycling with wind effect = (15+x)mph
distance traveled by Tara w wit wind = 16 miles
time taken by Tara while traveling with wind = 16/(15+x)
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it is given that both the time are same
time taken by Tara while traveling with wind = time taken by Tara while traveling against wind
16/(15+x) = 10/(15-x)
=> 16(15-x)=10(15+x)
=> 240 - 16x = 150 +10x
=>240 - 150 = 10x+16x
=> 90 = 26x
=> x = 90/26 = 3.46
Thus, speed of wind is 3.46 mph.
