Peter 16

Peter travels to his uncle's home, 30 km away from his place. He cycles for 2/3 of the journey before the cycle develops a mechanical problem, and he has to push it for the rest of the journey. If he is cycling 10 km per hour faster than his walking speed and completes the journey in 3hrs 20mins, determine his cycling speed.

Correct answer:

v =  15 km/h

Step-by-step explanation:

s=30 km t=3:20=3 hr 20 min =3+6020=3.3333 hr3.3333  s1=32 s=32 30=32 30=360=20 km s2=ss1=3020=10 km  v=10+p v t1 = s1 p t2 = s2 t1+t2= t  v t1 = s1 (v10) t2 = s2  v (tt2) = 20  km v t210 t2 = 10  km  20/(tt2) t210 t2 = 10  km  s1 xs2 x (tx)=s2 (tx)  20 x10 x (3.3333333333333x)=10 (3.3333333333333x) 10x23.333x33.333=0  a=10;b=3.333;c=33.333 D=b24ac=3.3332410(33.333)=1344.4444444444 D>0  x1,2=2ab±D=203.33±1344.44 x1,2=0.166667±1.833333 x1=2 x2=1.666666667  t2=x1=2 h t1=tt2=3.33332=341.3333 h  p=s2/t2=10/2=5 km/h v=s1/t1=20/1.3333=15   Verifying Solution:  T1=vs1=1520=341.3333 h T2=ps2=510=2 h T=T1+T2=1.3333+2=3103.3333 h

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