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Question Number 75439 by otchereabdullai@gmail.com last updated on 11/Dec/19
A man left his office in a car at 10am  to restaurant 30km away. He expected  to arrive at 11:10am but had to stop   15km from the office for 15 minutes .  He arrived at the restaurant 5 minutes   late.  a. Find the initial speed  b. Draw a travel graph for the whole journey
$$\mathrm{A}\:\mathrm{man}\:\mathrm{left}\:\mathrm{his}\:\mathrm{office}\:\mathrm{in}\:\mathrm{a}\:\mathrm{car}\:\mathrm{at}\:\mathrm{10am} \\ $$$$\mathrm{to}\:\mathrm{restaurant}\:\mathrm{30km}\:\mathrm{away}.\:\mathrm{He}\:\mathrm{expected} \\ $$$$\mathrm{to}\:\mathrm{arrive}\:\mathrm{at}\:\mathrm{11}:\mathrm{10am}\:\mathrm{but}\:\mathrm{had}\:\mathrm{to}\:\mathrm{stop}\: \\ $$$$\mathrm{15km}\:\mathrm{from}\:\mathrm{the}\:\mathrm{office}\:\mathrm{for}\:\mathrm{15}\:\mathrm{minutes}\:. \\ $$$$\mathrm{He}\:\mathrm{arrived}\:\mathrm{at}\:\mathrm{the}\:\mathrm{restaurant}\:\mathrm{5}\:\mathrm{minutes}\: \\ $$$$\mathrm{late}. \\ $$$$\mathrm{a}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{speed} \\ $$$$\mathrm{b}.\:\mathrm{Draw}\:\mathrm{a}\:\mathrm{travel}\:\mathrm{graph}\:\mathrm{for}\:\mathrm{the}\:\mathrm{whole}\:\mathrm{journey} \\ $$
Answered by MJS last updated on 11/Dec/19
first speed  30km in (7/6)hr ⇒ ((180)/7)km/hr≈25.7km/hr  first 15km in 35 minutes  second 15km in 35+5−15=25minutes  second speed ((15km)/(((25)/(60))hr))=36km/hr
$$\mathrm{first}\:\mathrm{speed} \\ $$$$\mathrm{30km}\:\mathrm{in}\:\frac{\mathrm{7}}{\mathrm{6}}\mathrm{hr}\:\Rightarrow\:\frac{\mathrm{180}}{\mathrm{7}}\mathrm{km}/\mathrm{hr}\approx\mathrm{25}.\mathrm{7km}/\mathrm{hr} \\ $$$$\mathrm{first}\:\mathrm{15km}\:\mathrm{in}\:\mathrm{35}\:\mathrm{minutes} \\ $$$$\mathrm{second}\:\mathrm{15km}\:\mathrm{in}\:\mathrm{35}+\mathrm{5}−\mathrm{15}=\mathrm{25minutes} \\ $$$$\mathrm{second}\:\mathrm{speed}\:\frac{\mathrm{15km}}{\frac{\mathrm{25}}{\mathrm{60}}\mathrm{hr}}=\mathrm{36km}/\mathrm{hr} \\ $$
Commented by otchereabdullai@gmail.com last updated on 11/Dec/19
God bless you prof MJS
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{prof}\:\mathrm{MJS} \\ $$

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