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Question
When the speed is increased by 4 miles per hour, it takes 4 hour less to cover a distance of 32 km. Find the previous speed.
8 km
4 km
12 km
2 km
ANSWER : 2
Descrption
<p style="margin-left:0px;">Let's denote the original speed as "x" miles per hour.</p><p style="margin-left:0px;">When the speed is increased by 4 miles per hour, the new speed becomes "x + 4" miles per hour.</p><p style="margin-left:0px;">We are given that when the speed is increased by 4 miles per hour, it takes 4 hours less to cover a distance of 32 km. We can set up the equation using the formula:</p><p style="margin-left:0px;">Time = Distance / Speed</p><p style="margin-left:0px;">Original time = 32 km / x New time = 32 km / (x + 4)</p><p style="margin-left:0px;">According to the given information, the new time is 4 hours less than the original time. So, we can write:</p><p style="margin-left:0px;">Original time - New time = 4 hours</p><p style="margin-left:0px;">32 km / x - 32 km / (x + 4) = 4</p><p style="margin-left:0px;">To solve this equation, let's first find a common denominator, which is x(x + 4):</p><p style="margin-left:0px;">(32(x + 4) - 32x) / (x(x + 4)) = 4</p><p style="margin-left:0px;">Now, simplify the equation:</p><p style="margin-left:0px;">(32x + 128 - 32x) / (x(x + 4)) = 4</p><p style="margin-left:0px;">128 / (x(x + 4)) = 4</p><p style="margin-left:0px;">Now, cross-multiply:</p><p style="margin-left:0px;">128 = 4(x(x + 4))</p><p style="margin-left:0px;">Divide both sides by 4:</p><p style="margin-left:0px;">32 = x(x + 4)</p><p style="margin-left:0px;">Now, let's solve for x by factoring:</p><p style="margin-left:0px;">x(x + 4) = 32</p><p style="margin-left:0px;">x² + 4x - 32 = 0</p><p style="margin-left:0px;">Now, we can factor the quadratic equation:</p><p style="margin-left:0px;">(x + 8)(x - 4) = 0</p><p style="margin-left:0px;">Setting each factor equal to zero:</p><p style="margin-left:0px;">x + 8 = 0 or x - 4 = 0</p><p style="margin-left:0px;">If x + 8 = 0, then x = -8, but since we're looking for a speed, it must be positive.</p><p style="margin-left:0px;">If x - 4 = 0, then x = 4.</p><p style="margin-left:0px;">So, the previous speed (original speed) was 4 km per hour.</p>
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