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Question

# A motor boat can travel 30 km upstream and 28 km downstream in 7 h. It can travel 21 km upstream and return in 5 h. find the speed of the boat in still water and the speed of the stream.

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Solution

## Let the speed of the motorboat in still water and the speed of the stream are u km/h and v km/h respectively Then, a motor boat speed in downstream = (u – v) km/h Motorboat has taken time to travel 30 km upstream t1=30u−vh and motor boat has taken time to travel 28 km downstream t2=28u+vh by first condition, a motor boat can travel 30 km upstream and 28 km down stream in 7 h i.e., t1+t2 = 7h ⇒30u−v+28u+v=7 ...eq(i) Now, motor boat has taken time to travel 21 km upstream and return i.e., t3=21u−v (upstream) (for downstream) And t4=21u+v By second condition, t4+t3=5h ⇒21u−v+21u+v=5 ...eq(ii) Let x=1u−v and y=1u+v Eqs. (i) and (ii) becomes 30x + 28y = 7 ...eq(iii) and 21x + 21y = 5 ⇒ x+y=521 ...eq(iv) Now, multiplying in Eq. (iv) by 28 and then subtracting from Eq. (iii), we get 30x + 28y = 7 28x + 28y = 14021 2x=7−203=21−203 2x=13⇒x=16 On putting the value of x in Eq, (iv), we get 16+y=521 ⇒y=521−16=10−742=342⇒114 ∴x=1u−v=16⇒u−v=6 ...eq(v) And y=1u+v=114 ⇒ u+v=14 ...eq(vi) Now, adding Eqs. (v) and (vi), we get 2u = 20 ⇒ u = 10 On putting the value of u in eq (v), we get 10 - v = 6 ⇒ v = 4 Hence, the speed of the motorboat in still water is 10 km/h and the speed of the stream 4 km/h

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