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Pls ans ques 3 and 4

Line segments OP, OA and OQ, in the figure above, coincide at the time t = 0 second. At the same instant of time, OP and OQ rotate in the plane about point O in opposite directions while OA remains fixed. With respect to OA, segment OP rotates at a constant rate of 4°per second and segment OQ rotates at a constant rate of 5° per second.

Q3. What is the smallest positive value of t, in seconds, for which segments OP and OQ will coincide?

Q4. When t = 1 hour, how many more revolutions does segment OQ complete than segment OP?
Pls ans ques 3 and 4

Line segments OP, OA and OQ, in the figure above, coincide at the time t = 0 second. At the same instant of time, OP and OQ rotate in the plane about point O in opposite directions while OA remains fixed. With respect to OA, segment OP rotates at a constant rate of 4°per second and segment OQ rotates at a constant rate of 5° per second.

Q3. What is the smallest positive value of t, in seconds, for which segments OP and OQ will coincide?

Q4. When t = 1 hour, how many more revolutions does segment OQ complete than segment OP?

$AnglecoveredbyOPin1second=4\xb0\phantom{\rule{0ex}{0ex}}AnglecoveredbyOPintseconds=4t\xb0\phantom{\rule{0ex}{0ex}}AnglecoveredbyOQin1second=5\xb0\phantom{\rule{0ex}{0ex}}AnglecoveredbyOQintseconds=5t\xb0\phantom{\rule{0ex}{0ex}}SinceOPandOQmovesinoppositedirection,\phantom{\rule{0ex}{0ex}}\therefore 4t+5t=360\phantom{\rule{0ex}{0ex}}(addingtwoanglesbecausetheyareapproachingeachother,andtotalangleofcircle=360\xb0)\phantom{\rule{0ex}{0ex}}\Rightarrow 9t=360\phantom{\rule{0ex}{0ex}}\Rightarrow t=\frac{360}{9}=40\phantom{\rule{0ex}{0ex}}Thust=40secondswhentheycoicideeachother.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Whent=1hour=60seconds\phantom{\rule{0ex}{0ex}}OPcovers=4t=4\times 60=240\xb0\phantom{\rule{0ex}{0ex}}OQcovers=5t=5\times 60=300\xb0\phantom{\rule{0ex}{0ex}}ThusOQcovers60\xb0morethanOP.$

Regards

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