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DerKrebs [107]
3 years ago
9

A car travels for 4(t+3) hours at a constant speed of 10(t+3) km/h. If the total distance travelled by the car is 810 km, find t

he speed of the car.
Mathematics
1 answer:
IceJOKER [234]3 years ago
3 0

Step-by-step explanation:

\because \: time \times speed  = distance \\  \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \:  \{2(t + 3) \}^{2} =  {9}^{2}  \\  \therefore \:  \{2(t + 3) \} =  {9}   \\  \therefore \: t + 3 =  \frac{9}{2}  \\ \therefore \: t  =  \frac{9}{2}  - 3 \\  \therefore \: t  =  \frac{9 - 6}{2}  \\  \therefore \: t  =  \frac{3}{2}  \\ \therefore \: t  =  1.5 \: hrs  \\

\because \: time \times speed  = distance \\  \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \:  \{2(t + 3) \}^{2} =  {9}^{2}  \\  \therefore \:  \{2(t + 3) \} =  {9}   \\  \therefore \: t + 3 =  \frac{9}{2}  \\ \therefore \: t  =  \frac{9}{2}  - 3 \\  \therefore \: t  =  \frac{9 - 6}{2}  \\  \therefore \: t  =  \frac{3}{2}  \\ \therefore \: t  =  1.5 \: hrs  \\ speed \: of \: car = 10(t + 3) \\ \hspace{60 pt} = 10(1.5 + 3) \\   \hspace{60 pt}= 10 \times 4.5 \\ \red{ \boxed{ \bold{ \therefore \: speed \: of \: car  = 45 \:km/ h}}} \\

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