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| 1. |
ut 302 and -3V215. A motor boat can travel 30km upstream and 28km downstream in 7 hours. I cartravel 21km upstream and return in 5hours. Find the speed of the boat 13 still wateand the speed of the stream. |
| Answer» <p>Let the speed of the boat in still water = xkm/hr.</p><p>Let the speed of the stream = ykm/hr.</p><p>Speed upstream = x - y.</p><p>Speed Downstream = x + y.</p><p>Now,</p><p>Given that boat can travel 30km upstream and 28km downstream in 7 hours.</p><p>30/x-y + 28/x+y = 7 </p><p>Let 1/x - y = a and 1/x + y = b</p><p>30a + 28b = 7 ---------------------------- (1).</p><p>Also, Given that it can travel 21 km upstream and return in 5 hours.</p><p>21/x - y + 21/x + y = 5</p><p>Let 1/x - y = a and 1/x + y = b</p><p>21a + 21b = 5 ------------------------ (2)</p><p>On solving (1) * 21 & (2) * 28, we get</p><p>630a + 588b = 147</p><p>588a + 588b = 140-----------------------------42a = 7</p><p>a = 1/6.</p><p>Substitute a = 6 in (1), we get</p><p>30a + 28b = 7</p><p>30(1/6) + 28b = 7</p><p>5 + 28b = 7</p><p>28b = 7 - 5</p><p>28b =2</p><p>b = 2/28</p><p>b = 1/14.</p><p>We know that,</p><p>a = 1/x - y</p><p>1/6 = 1/x - y</p><p>x - y = 6 ----------- (3)</p><p>We know that,</p><p>a = 1/x - y</p><p>1/6 = 1/x - y</p><p>x - y = 6 ----------- (3)</p><p>We know that,</p><p>b = 1/x + y</p><p>1/14 = 1/x + y</p><p>x + y = 14 ------------ (4).</p><p>On solving (3) & (4), we get,</p><p>x + y = 14</p><p>x - y = 6</p><p>------------</p><p>2x = 20</p><p>x = 10</p><p>Substitute x = 10 in (4), we get</p><p>x + y = 14</p><p>10 + y = 14</p><p>y = 14 - 10</p><p>y = 4.</p><p>Therefore the speed of the boat in still water = 10km/hr.</p><p>Therefore the speed of the stream = 4km/hr.</p> | |