A car takes p minutes to travel a distance of 350km with an average speed of ukm∕hr. Another car takes q minutes to travel the same distance with an average speed of vm∕hr. If u−v=5 and q−p=140, then what is the value of u ?
Given: A car takes p minutes to travel 350km with an average speed of um∕hr. Another car takes q minutes to travel 350km with an average speed of vm∕hr. u−v=5‌⋯−(i) q−p=140‌‌⋯(‌ (ii) ‌ Concept Used: Distance = Speed × Time If the distance covered is constant then Product of speed and time is also constant Calculation: According to the question The total distance covered by both the car is constant u×p=v×q ⇒v∕u=p∕q Using Componendo rule we get ⇒(u−v)∕u=(q−p)∕q ⇒5∕u=140∕q ⇒q=28u‌‌−‌‌−‌ (iii) ‌ Now, According to the question u×p×(1∕60)=350 ⇒u×p=21000 And Also v ×q×(1∕60)=350 ⇒v×q=21000‌‌⋯(v) From (i), v=u−5‌‌⋯(vi) From (ii), p=q−140‌‌⋯ (vii) From (iv) and (vii), we get ⇒u×(q−140)=21000 ⇒uq=21000+140u Now, from (iii), we get ⇒uq=21000+140u ⇒u×28u=21000+140u ⇒28u2−140u−21000=0 ⇒u2−5u−750=0 ⇒u2−30u+25u−750=0 ⇒u(u−30)+25(u−30)=0 ⇒(u−30)(u+25)=0 u=30,u=−25 [not possible ] ∴ The value of u is 30km∕hl :